Session 4
�Physical properties of tropical sandy soils”

Physical properties of tropical sandy soils: A large range of behaviours

Bruand, A.¹; C. Hartmann² and G. Lesturgez^{2, 3}

Introduction

Sandy soils are characterized by less than 18% clay and more than 68% sand in the first 100 cm of the solum. In the World Reference Base (WRB) soil classification system (ISSS Working Group R.B. 1998), sandy soils may occur in the following Reference Soil Groups: Arenosols, Regosols, Leptosols and Fluvisols. These soils have developed in recently deposited sand materials such as alluvium or dunes. They are weakly developed and show poor horizonation. Soils characterized by a high proportion of sand in the first 100cm can also correspond to the upper part of highly developed soils formed in weathered quartz-rich material or rock, as evidence by the development of a highly depleted horizon. In the following discussion consideration will be given to a range of soils including sandy soils of the WRB and those with sandy horizons in the upper 100cm of the profile.

Sandy soils are often considered as soils with physical properties easy to define: weak structure or no structure, poor water retention properties, high permeability, highly sensitivity to compaction with many adverse consequences. However, analysis of the literature shows that their physical properties are far from simple. This is particularly true in the tropics where sandy soils are subjected to a cycle of wetting and drying that greatly affects the soil with small differences in composition leading to significant differences of physical properties.

Structure, porosity and bulk density

Sandy soils are characterized by a lack of structure or that it is weakly development. Coquet (1995) measured the shrinkage properties of two soils in Senegal with different texture. On the sandy soil, results obtained in the field and in the laboratory (on cores originating from the same horizons), showed very small shrinkage: bulk volume variation was only 0.05%. When they dried, sandy soils develop very few thin cracks organised in a loose network. The meagre shrinkage properties of these soils are related to the low clay content and the high proportion of low activity clays of many tropical sandy soils.

A large range of porosity

Sandy soils in the tropics show a large range of porosities and consequently bulk density (D_b). Porosity ranges from 33% (D_b = 1.78 g cm^-3) to 47% (D_b = 1.40gcm ^-3) are commonly recorded (Figure 1). The porosity in sandy soils is usually smaller than in clayey and silty soils.

Figure 1. Variation of porosity according to the sand content in tropical sandy soils (after Nicou, 1974 and 1976; Chauvel, 1977; Coquet, 1995; Lamotte et al., 1997a; Burt et al., 2001; Nyamangara et al., 2001; Feng et al., 2002; Bortoluzzi, 2003; Bruand et al., 2004; Lesturgez, 2005; Osunbitam et al., 2005)

Very small changes in porosities are generally observed in sandy soils of the tropics. Lamotte et al. (1997a and b) observed a porosity of 28% (D_b = 1.91 gcm ^-3) between 35 and 45 cm depth in the Northern Cameroon’s in very old cultivated fields. Lesturgez (2005) measured a porosity of 28% between 20 and 30 cm depth in a soil belonging to the Warin-Satuk series in Northern Thailand in cultivated soils. Deeper in the soil, similar small porosities were recorded by Burt et al. (2001) in sandy soils developed in a saprolithe derived from granitic rocks in Zimbabwe. These small porosities were recorded in sandy soils with no gravel or stones thus indicating a close packing of elementary soil particles in soils that have been subjected to continuous cultivation.

However, under native vegetation with intense biological activity or after recent tillage operation (wheel tracks excluded), greater porosity of 60% (D_b = 1.10 gcm ^-3) have also been recorded (Bortoluzzi, 2003; Lesturgez, 2005). Such a large porosity is related to the presence of numerous macropores that results from both faunal activity and root development. Bruand et al. (2004) have also observed greater porosity in the subsoil of intensively cultivated soils, this being related to a loose assemblage of elementary soil particles unaffected by farming practices.

Significance of sand and silt grain size distribution

Porosity varies with time after tillage operations thus making it difficult to attribute to soil composition alone. Osunbitan et al. (2005) showed a continuous decrease in the porosity of the 0-5 cm layer of a Nigerian loamy sand soil. Porosity ranged from 47.7% (D_b = 1.30 gcm ^-3) to 60.4% (D_b = 1.05 gcm ^-3) according to the tillage system and time after tillage. If we exclude the topsoil horizons from the dataset used in Figure 1, Figure 2 indicates that the finesand: coarsesand ratio ranges from 0.5 to 6.1 for the data collected in the literature and the porosity tends to decrease when ratio increases (R² = 0.40, n=55). The fine sand particles occupying the voids resulting from the packing of the coarse particles would result in the porosity decreasing when the proportion of fine sand particles increases up to a value that would correspond to the total infilling of that void. With a greater proportion of fine sand, the porosity would start again to increase. An increase in the silt-sand ratio wouldalso result in a decrease in the porosity as discussed by Agrawal (1991) for Indian loamy sand and sandy loam soils.

Figure 2. Relationship between the fine sand and coarse sand ratio (after Nicou, 1974; Chauvel, 1977; Coquet, 1995; Lamotte et al., 1997a; Nyamangara et al., 2001; Feng et al., 2002; Bortoluzzi, 2003; Bruand et al., 2004; Lesturgez, 2005)

Figure 3. Porosity recorded for a mixture of silt (20-50 µm) and coarse sand (2 mm) particles according to the coarse sand proportion (modified after Fiès et al., 1972)

These data recorded with soils samples are consistent with those obtained earlier with models and artificial mixtures in the laboratory (Fiès, 1971; Fiès et al., 1972; Panayiotopoulos and Mullins, 1985). Fiès et al. (1972) studied the porosity of granular binary mixture and modelled porosity according to the proportion of coarse and fine fractions. They showed that for a mixture of 20-50 µm material with grains 2 mm in diameter, the porosity is minimum (P ≈0.20) for 20-50 µm material content close to 25% (Figure 3). That proportion of fine material is consistent with the theory developed by Westman and Hugill (1930). They calculated an optimum ratio of 3.46 parts by mass of coarse sand to one part of very fine sand (i.e. 22.4% on mass basis of very fine sand) was required to obtain a mixture with the lowest porosity. Fiès and Stengel (1981) showed good concordance between porosity measured on small aggregates resulting from soil fragmentation and theoretical porosity computed with a model of binary mixtures. In particular, they showed that the porosity was at a minimum for a mixture of 2-20 µm and 200-2,000 µm when 2-20 µm content was close to 20% (Figure 4). These data indicate that the loose relationship shown in Figure 2 between the porosity and the fine sand and coarse sand ratio would be valid for a limited range of fine sand and coarse sand ratio.

Role of the clay fraction characteristics

The large range of porosity (Figure 1) is related to the small cohesion forces between elementary particles thus enabling the formation of a large range of assemblages from very loose to very compact. This is specific to sandy soils because of the small amount of clay that can act as inter-grain cement. In the tropics, clay is often low activity clay (mainly kaolinite) and for similar clay content, tropical sandy soils show usually much smaller inter-grain cohesion than sandy soils in temperate and Mediterranean regions (van Wambeke, 1992). In these deeply weathered soils, the clay-sized fraction may in part consist of quartz as observed by Hardy (1993) in soils that developed in sandy colluvial deposits in Northern Vietnam. Hardy (1993) showed that 10 to 40% of the <2 µm fraction was quartz in the soils studied. Bruand et al. (2004) studied sandy soils belonging to the Nam Phong series in Northeast Thailand and found that 25 to 35% of the <2 µm fraction was quartz. The presence of quartz in the <2 µm fraction contributes to its low activity. In some sandy soils, however the presence of smectitic clays can lead to very different physical soil properties. In the semi-arid tropics, Lamotte et al. (1997) studied soil hardening in sandy soil with contrasting loose topsoil and underlying hard horizons. The horizons had similar particle size distributions and the hardness was closely related to a fabric with clay coatings on the sand grains and clay wall-shaped bridges linking the latter. This induced a strong continuity of the solid phase with only a minimum clay content of 6%.

Figure 4. Bulk density recorded by Fiès and Stengel (1981) according to the proportion of silt (20-50 µm) relative to the silt and sand particles (200-2,000 µm) in soils with clay content <20% and no macroporosity

Hydraulic properties

Water retention properties

Sandy soils retain little water at high water potentials and water content decreases rapidly with the water potential. Panayiotopoulos and Mullins (1985) studied the water retention properties of pure sand materials varying in size (Figure 5). They showed that most water was released between -0.1 and -1kPa for a coarse sand (2,000-710 µm) and between -15 and -30 kPa for a very fine sand (125-45 µm). The limited water release osbserved for the very fine sand between saturation and -0.5 kPa was not discussed by Panayiotopoulos and Mullins (1985). Mullins and Panayiotopoulos (1984) showed that the water retention curve was only very slightly affected by the clay content for a clay content <20%. The clay used was a kaolinite. With sandy soils, two thirds of the water present at saturation is usually released at -30 kPa as recorded by Obi and Ebo (1995) in a sandy soil in Southern Nigeria. Water contents ranging from 0.20 to 0.30cm ³cm ^-3 and from 0.04 to 0.12cm ³cm ^-3 are often recorded at -33 and -1500kPa, respectively in tropical soils belonging to the sand, loamy sand and sandy loam textural class (Hodnett and Tomasella, 2002). In sandy soils, there is very little water available at matric potential <-100 kPa. Kukal and Aggarwal (2004) measured a water content of 0.16 and 0.10 cm³ cm^-3 at -33 and -1500kPa, respectively in a sandy loam topsoil (% clay = 10%) in India. The water content significantly increased with a slight increase in the clay content and was 0.22 and 0.13 cm³cm ^-3 at -33 and -1500kPa, respectively when the clay content was 14%. Osunbitam et al. (2005) showed in Nigeria an averaged water loss in sandy soils of 0.006mm ^-3 between -100 and -150kPa, the water content at -150 kPa being 0.017mm ^-3. Several studies have shown that the available water increases with the silt content (Kapilevich et al., 1987; Agrawal, 1991).

Tomasella and Hodnett (1998) compared the measured volumetric water content at different matric potentials and those estimated with the pedotransfer functions (PTFs) developed by Rawls et al. (1992) from the USDA soil data base. They showed that these PTFs greatly overestimate the volumetric water content when applied to sandy soils of Brazilian Amazonia (Figure 6). The available water capacity measured between -5 and -1,500 kPa by Nyamangaraet al. (2001) in Zimbabwe for topsoils with a sand content close to 90% ranged from 0.159 to 0.174 m³m ^-3 according to cattle manure management options.

Figure 5. Water retention curves recorded for a coarse sand (hexagon, 2,000-710 µm), medium sand (diamond, 500-180 µm), fine sand (circle, 220-105 µm) and very fine sand (triangle, 125-45 µm) (modified after Panayiopoulos and Mullins, 1985)

Figure 6. Comparison between measured values of volumetric water content at -33 kPa water potential and those estimated by the pedotransfert functions of Rawls et al. (1982) (modified after Tomasella and Hodnett, 1998)

Hydraulic conductivity

The saturated hydraulic conductivity (K_s) of sandy soils in the tropics varies within a range of values covering several orders of magnitude (10^-7 <K_s <10^-3 ms ^-1). In a Brazilian sandy soil with very low clay contents (average content in the whole profile of 0.25%), Prevedello et al. (1995) measured 1.1 × 10^-6 <K_s <7.5 × 10^-5 m s^-1. Contrasting this in another Brazilian sandy soil with only a slight change in clay content (average content in the whole profile of 6%), Faria and Caramoni (1986) measured 1.5 × 10^-5 <K_s <2.8 × 10^-4 m s^-1.

In soils, K_s varies according to the development of the macroporosity. As a consequence, K_s variation is more closely related to the macroporosity development rather than to soil texture. Thus, most studies try to relate K_s to part of the macroporosity that is called effective porosity (Φ_e) and defined as total porosity, Φ minus the water content at -33 kPa (Ahuja et al., 1984). K_s and Φ_e are related as following: with B and n, are two parameters varying with the soil characteristics. These parameters were obtained by Tomasella and Hodnett (1997) for Brazilian tropical soils. They found log B=4.752 and n=4.536 for the soils studied by Predevello et al. (1995) and log B=4.758 and n=4.532 for soils studied by Faria and Caramoni (1986). These soils were also used by Tomasella and Hodnett (1997) to derive parameters of the Brook-Corey/Mualem model for unsaturated hydraulic conductivity.

However when cultivated, the macroporosity of sandy soils is very unstable and collapses rapidly in the presence of water. Thus, the measurement of K_s becomes difficult to perform without modifying the macroporosity that have a tremendous effect on K_s. This probably explains why many studies do not report a large range of K_s variation between field experimental treatments and with time as expected. Thus Osunbitan et al. (2005) recorded 5.5 <K_s <7.5 × 10^-5 ms ^-1 in a topsoil under different tillage treatments. The K_s difference recorded by these authors between the different treatments (1 × 10^-5 ms ^-1) was small and similar to the differences recorded under the same tillage treatment over a period of 8 weeks.

Unsaturated hydraulic conductivity (K_θ) of Brazilian sandy soils was also discussed by Tomasella and Hodnett (1997) (Figure 7).

Figure 7. Unsaturated hydraulic conductivity for a sandy soil with a porosity of 45 and 35% (computed after the data published by Tomasella and Hodnett, 1995)

Surface crusting and water infiltration

Because of the very small inter-particle cohesion that results in a very small aggregate stability, sandy soils are highly sensitive to surface crusting, thus explaining the large number of papers in this area (e.g. Chartres, 1992; Casenave and Valentin, 1992; Isbell, 1995; Bielders and Baveye, 1995a; Valentin and Bresson, 1998; Malan Issa et al., 1999; Duan et al., 2003; Eldridge and Leys, 2003; Janneau et al., 2003; Goossens, 2004;). Crusts protect the soil surface from wind and interrill erosion but they also favour runoff and consequently rill and gully erosion (Valentin and Bresson, 1998). Two main types of structural crusts were recognised in sandy soils depending on the dominant forming process (Casenave and Valentin, 1992; Valentin and Bresson, 1992; Janeau et al., 2003): (i) sieving crusts made of well sorted micro-layers with average infiltrability of approximately 30 mmh ^-1, (ii) and packing crusts made of sand grains closely packed with average infiltrability of 10 mmh ^-1. Bielders and Baveye (1995b) studied in the laboratory the processes of structural crust formation on coarse textured soils. They proposed that the formation of clay-band in sieving structural crusts would be initiated by the displacement of micro-aggregates or other small particles from the above washed-out layer, followed by their accumulation due to mechanical straining. Erosion crusts that result from smoothening and erosion of structural crusts and depositional crusts that result from sedimentation were also described (Valentin and Bresson, 1998). They exhibit more restrictive infiltrability (2-5 mm ^-h¹) than structural crusts.

The development of crusts leads to runoff that can be quite significant. Sombatpanit et al. (1995) measured between 300 and 400mm of runof f that corresponded to about 35% of the rainfall on bare sandy soils in Thailand with 25 to 70 tha ^-1 of soil loss. Runoff was still between 10 and 20% of the rainfall under different agricultural treatments.

Surface infiltrability can also be reduced in sandy soils by repellency. Indeed, sandy soils are particularly susceptible to water repellency and susceptibility increases with the duration of the dry season. Repellency is responsible for vertical fingered flow in sandy soils because of the presence of repellent soil volumes with hydrophobic organic matter (Roberts and Crabon, 1972; Dekker and Ritsema, 1994; Ritsema and Dekker, 1994). Study of repellent soils in arid and humid climates showed that repellency would be much more related to the type of organic matter than to the duration of the dry period (Jaramillo et al., 2000).

Compaction

Sensitivity to soil compaction

Unlike other soils, the structure of sandy soils can be easily affected by mechanical compaction over a large range of scales. Usually mechanical compaction preferentially affects large pores (i.e. macropores that result from tillage and biological activity) but in sandy soils it affects these large pores down to the small pores that result from the arrangement of the skeleton particles (sand and silt) within the clay fraction. That re-arrangement when submitted to mechanical compaction is possible because of the small cohesion between the skeleton particles. For narrowly graded pure sand materials, Panayiotopoulos and Mullins (1985) showed that these air-dry and nearly saturated sands were always found to pack more closely under a given load than the same sand at any water content.

Very small porosity can be recorded under wheel tracks and just underneath the tilled layer. Thus, Bennie and Botha (1986) recorded 1.7 <D_b <1.8gcm ^-3 in the 0-20 cm layer under wheel tracks and in the 20-40 cm layer. Because of this small inter-particle cohesion, high bulk density is also recorded when sandy soils are puddled in rice-wheat cropping systems. Thus, Aggarwal et al. (1995) recorded 1.75 <D_b <1.82gcm ^-3 in the 15-20 cm layer after several years of high puddling in a sandy loam soil.

Smith et al. (1997a) studied the effect of soil compaction on a large range of South African forestry soils. They showed on soil cores in the laboratory that the porosity after compaction of sandy loam and loamy sand soils was related to the size distribution of the sand fraction and tended to decrease with the increase in the clay and silt content. Smith et al. (1997b) showed for loamy sand that increases in compaction were almost independent of the water content and then almost entirely due to increasing applied pressure alone. Smith et al. (1997c) also recorded a high compactibility for sandy soils derived from sandstone, granite and aeolian sands. The maximum bulk density was related to the loss in mass after ignition at 450°C.

Penetration resistance

Increases in bulk density invariably results in an increase in the penetration resistance with significant consequences for root development although there no clear relationship with the penetration resistance (Mullins et al., 1987; Bengough and Mullins, 1991). Critical values that severely restrict root growth have been estimated to vary from <1 to >4 MPa depending on the soil, water content and crop type (Greacen et al., 1968). Indeed, the penetration resistance varies within a large range of values according to the soil water content without any variation of the other soil characteristics (e.g. particle size distribution, mineralogy, porosity, assemblage of the elementary particles). It is significantly inversely related to water content. Many penetration resistances published in the literature for sandy soils range between 0.1 and 0.8 MPa but the water content at which they were determined often remains unclear (Osunbitan et al., 2005). Bruand et al. (2005) recorded a penetration resistance ranging from 0.35 to 0.55MPa in the subsoil of a sandy soil in Thailand when the water content ranged from 0.03 to 0.09kgkg ^-1 (Figure 8). In South African sandy soils that developed in aeolian sand, Du Preez et al. (1981) measured penetration resistance >1.5MPa, at field moisture capacity, in a ploughed layer under wheel tracks. In these soils Bennie and Botha (1986) confirmed the presence of such values of resistance to penetration in the subsoil and showed that they result from compaction because of traffic that leads to an increase in the penetration resistance that restricts root development for wheat and maize. Kukal and Aggarwal (2003) measured much greater penetration resistance in a sandy loam soil after puddling because of subsurface compaction. Indeed, these authors recorded at field capacity a penetration resistance ranging from 3.0 to 4.5 MPa in the compacted layer.

Figure 8. Resistance to penetration expressed as unconfined strength with respect to water content in the Ap (square), E (circle) and Bt (triangle) horizons. (modified after Bruand et al., 2005)

In their study, Smith et al. (1997a) showed on compressed soil cores only small differences in strength development across a wide range of water content for a loamy sand soil. This would be related to the contribution of frictional rather than cohesion forces to resistance to penetration (Smith et al., 1997a). On the other hand, results also showed somewhat different behaviour for a sandy loam soil, resistance to penetration increasing from 1 to 5 MPa over a range of water content of only 4% by mass. This large range of resistance to penetration would result from the contribution of cohesion forces that are partly related to the water content. Thus, a decrease in water content would increase frictional and cohesion forces from field capacity to intermediate water content, smaller water contents increasing the frictional forces alone, the cohesion forces disappearing, thus explaining the results recorded in Nigeria by Ley et al. (1995) on a large range of soils including sandy soils.

Effect of combined deep tillage and controlled traffic on penetration resistance and its consequences for root growth has been studied in several countries. In their one-year study, Bennie and Botha (1986) showed that deep ripping and controlled traffic led to a significant increase in rooting depth, rooting density in the subsoil, water use efficiency and yield increases of 30% for maize and 19% for wheat. Increased yields were recorded in many earlier studies after deep tillage (e.g. Reicosky et al., 1976; Bennie et al., 1985) but the duration of the positive effects of deep tillage is still under discussion. Slotting was also used to loosen the subsoil in sandy soils of Northeast Thailand and thus promoted rooting (Jayardanne et al., 1995). Hartmann et al. (1999) showed that rooting depth and yield of various crops were increased for two successive years after slotting. Lesturgez (2005) recorded a significant increase in root density in the slot that enables a better subsoil exploitation. Lesturgez et al. (2004) also investigated the potential use of forage legume Stylosanthes hamata (stylo) to ameliorate the structure of compact layers in sandy soils of Northeast Thailand. They showed that after 24 months of continuous stylo, roots were able to penetrate the compact subsoil, resulting in an improvement of its macroporosity. They also showed that a subsequent maize crop developed a deep and extensive root system using the macropores.

Hardsetting in sandy soils

Many tropical sandy soils are potentially hardsetting soils, i.e. they can become compact, hard with apparently apedal condition prevailing on drying (Northcote, 1979). In these soils, a significant increase in soil strength is recorded over very narrow water content changes within the plant available range of soil water potential (-10² to -10³kPa) with resulting adverse effects on root growth and crop production (Mullins et al., 1990). Thus, Chan (1995) measured strength characteristics in sandy loam hardsetting soil in the semi-arid region of Australia and showed that in the cultivated soil strength increased from 0.02 to 0.09 MPa with decreasing water content from 0.11 to 0.04 kgkg ^-1 when there was no strength variation under permanent pasture. McKyes et al. (1994) studied the cohesion and friction in two sandy-loam hardsetting soils from Zimbabwe. They showed that the cohesion changed from nearly zero at saturation to well over 0.1 MPa in the field dry state. Young and Mullins (1991) suggested that the amount of <60 µm particles rather than solely the <2 µm is important in causing the development of hardsetting properties.

High soil strength in sandy soils can be also partly related to the development silica precipitation that forms globules and silica flowers over the sand grains (Lesturgez, 2005). These precipitations would not be responsible for a cementation of the sand and silt grains but would lead to an increase in particle contacts and frictions, thus explaining the increase in soil strength recorded.

Controlled compaction

Compaction in sandy soils was also discussed as a possible water and nutrient management to improve water retention properties and reduce nutrient leaching in Indian sandy soils (Agrawal and Kunar, 1976; Agrawal et al., 1987; Agrawal, 1991; Arora et al., 2005). Indeed, according to these authors, compaction that reduces the volume and continuity of large pores, would increase water retention and reduce water infiltration and saturated hydraulic conductivity in highly permeable deep sandy soils. Compaction would save irrigation water by 15-36% and increase productivity by 30-50%.

Puddling is also used to reduce high percolation losses of irrigation water and nutrient leaching when cultivated for rice production (Aggarwal et al., 1995; Arora et al., 1995). Sharma and Bhagat (1993) showed that puddling was effective in reducing percolation losses when sand was less than 70%, and finer fractions were dominated by clay (13-20%). Puddling has been reported to decrease saturated hydraulic conductivity of the puddled layer (0-10cm) of sandy loam soil from 1.810 ^-7 ms ^-1 in unpuddled to 4.210 ^-8ms ^-1 with medium puddling and 2.510 ^-8ms ^-1 with highly puddle soils (Kukal and Aggarwal, 2002). Kukal and Aggarwal (2003b) showed in a sandy loam soil that puddling reduced percolation losses by 14-16% with the increase in puddling intensity from medium to high, whereas the amount of irrigation water required decreased by 15-25%. Similar results were recorded by Kukal and Sidhu (2004) in another sandy loam soil in India.

However, puddling in rice-wheat cropping systems leads to some adverse effects for the following wheat crop that requires to be managed with appropriate tillage techniques (Aggarwal et al., 1995; Kukal and Aggarwal, 2003a; Arora et al., 2005).

A yield decline of wheat is often recorded because of subsurface compaction (1.70 <D_b <1.75 gcm ^-3) at 14-20 cm depth under normal puddling at normal depth. Kukal and Aggarwal (2003a) showed in India for a sandy loam soil that puddling at shallow depth (5-6 cm) led to the development of a compact layer at 10-12 cm depth that was loosened (1.50 <D_b <1.55 g cm^-3) during normal cultivation for wheat seedbed preparation

Conclusion

In the tropics, physical attributes of sandy soils are particularly sensitive to both the sand and silt size distribution and mineralogy of the clay fraction. Because of the presence of low activity clay in most sandy soils, the assemblage of elementary skeleton particles is highly unstable resulting in a high instability with respect to structure from the microscopic to macroscopic scale. When for a variety reasons, the assemblage collapses, the resulting porosity and penetration resistance would be all the greater as the skeleton particle distribution is heterometric.

In contrast, in sandy soils unlike other soils, the elementary fabric can be easily loosened by tillage practices. Thus greater porosity can be produced easily by tillage but its stability is very weak and compaction by wheels or other actions can produce a dense structure with adverse physical properties. This leads to a decrease in the water retention properties and hydraulic conductivity, an increase in the resistance to penetration and sensitivity to surface crusting.

More generally, tropical sandy soils, more than other soils, require careful management in an environmentally friendly manner. Indeed, even if most physical degradation processes are more easily reversible in tropical sandy soils than in other soils, the physical fertility of these soils is weak. These soils require very little tillage operations in the wrong way to produce significant adverse consequences for plant development and consequently for crop yield and environment.

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¹ ISTO, Institut des Sciences de la Terre d’Orléans, UMR 6113 CNRS UO, Université d’Orléans, Géosciences BP 6759 45067, Orléans Cedex 2, France, [email protected]
² IRD, UMR 7618 BIOEMCO, Laboratoire de Biogéochimie et Ecologie des Milieux Continentaux, 46 rue d’Ulm, 75230 Paris Cedex 05, France
³ INRA, Unité de Science du Sol, Centre de Versailles, Route de St Cyr, 78850 Versailles cedex, France.

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

Introduction

Soil compaction in agricultural systems is a worldwide concern and has received considerable attention over the past decades (Soane and van Ouwerkerk, 1994; Hamza and Anderson, 2005). Soil compaction is defined as: “the process by which soil grains are rearranged to decrease void space and bring them into closer contact with one another, thereby increasing the bulk density” (Soil Science Society of America, 1996). The vast majority of soil compaction in modern agriculture is often attributed to heavy machinery and traffic load (Flowers and Lal, 1998). However other processes can be involved and soil compaction may occur without traffic load on soil surface. For example, the formation of a dense subsoil layer known as “fragipan” is interpreted by soil collapse under its own weight. This process occurs when a metastable arrangement of particles is wetted under a constant confining pressure (weight of the top layer in the case of natural collapse) (Assallay et al., 1997; 1998).

Sandy soils are often considered as structurally inert because of their weak structure and the absence of shrink-swell properties but frequent and severe compaction observed in agricultural fields raises the question of the processes and factors that control soil compaction and its reversibility. In the sandy upland soils of Northeast Thailand, subsoil compaction (20-40 cm) is a common feature that impairs root development and therefore is responsible for low crop production (Bruand et al., 2004). Comparisons between forest and adjacent cultivated area have proved that the compact layer commonly observed in agricultural fields was induced by intensive agriculture of the last decades (Lesturgez, 2005). Sandy soils of the region have developed mainly from light textured aeolian material (Boonsener, 1991) well known for its problematic characteristics for engineering works (Udomchoke, 1991; Kohgo et al., 2000). On the other hand, deep ploughing and subsoiling have always been inefficient in overcoming this compaction in agricultural systems since soil re-compacts after the first heavy rain. This suggest that collapsibility is a key factor not only in deep profiles but also in the superficial 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 the formation or the reformation of a compact layer. The objective of the study was to investigate the processes of soil compaction in a tilled sandy soil subjected to non-flooding rains and evaluate their respective contribution to total soil compaction. Experiments focussed on uniaxial compactability, hydrocollapse and rearrangement under traffic load.

Material and methods

Soil characteristics and sampling

The samples were collected in a sugarcane field located in Ban Phai District, 40-km from Khon Kaen City, Northeast Thailand (16°08′N, 102°44′E). The choice of the site was based on a previous investigation that highlighted the presence of a compact layer located at 20-40 cm depth that was representative of the general situation of subsoil compaction (Lesturgez, 2005). The soil has a sandy texture with no or very weak structure. It belongs to the Nam Phong soil series (Imsamut and Boonsompoppan, 1999) and was classified as a loamy, siliceous, isohyperthermic Arenic Haplustalf (Soil Survey Staff, 1998) or Arenic Acrisol (FAO, 1998). Three undisturbed samples were collected from the vertical face of a pit, respectively in the topsoil (0-15 cm), in the compact subsoil (15-25 cm) and underneath the compact layer (40-50cm). Selected chemical and physical characteristics of the samples are presented in Table1. Mineralogical characteristics of the studied soil were investigated using X-ray diffraction. When the sand and silt fractions were exclusively constituted of quartz, the clay fraction included kaolinite, traces of illite and a significant proportion of small quartz particles. The three samples were identical in their mineralogy and the particle size distribution of the sand fraction. They differed only in their clay content (from 70gkg ^-1 in the topsoil to 136 g kg^-1 in the deepest layer). A last sample (pure sand material) was prepared from the topsoil horizon by sieving the >50 µm material from the whole soil after dispersion in sodium hexametaphosphate.

Sample preparation

The samples were manually crumbled in the laboratory in order to produce small aggregates similar to tillage-induced aggregates. The aggregates were poured into a ring 50mm in diameter , and 18mm in height placed on a porous plate using a small funnel fixed 5-cm above the middle of the ring. The ring was overfilled, then the surface was carefully levelled off, and the assemblage thoroughly cleaned with a small brush. The assemblage was then installed in the oedometer and the top cap gently positioned. Preliminary tests had shown that the preparation of the aggregate beds using this method allowed the formation of a metastable arrangement of aggregates with a bulk density similar to that of the topsoil after ploughing.

Design of the oedometer apparatus

The oedometer test is classically used for consolidation and compression studies of fine-grained soil samples, such as clays and silts, since it recreates the conditions of volume change with zero lateral strain (i.e. one-dimensional compression). The oedometer apparatus used (Figure 1) allows the application of an axial load that ranges from 0 to 1,500 kPa. We applied 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, 1,300 and 1,500 kPa), with 5 minutes interval between each step (minimum duration to reach equilibrium). The change in volume of the samples was recorded continuously by measuring the vertical displacement of the rigid top platen used to apply the load. The design of the apparatus allows the injection of water on the top of the sample. Drainage was free through the porous plate located below the sample. The volume of water injected into and drained from the samples can also be recorded. Bulk density and average water content were derived from these measurements. The background noise of the oedometer originating from internal deformation (porous plates) and elasticity of the membrane was estimated during preliminary tests on uncompressible Plexiglas cylinders and results were corrected accordingly.

Figure 1. Oedometer apparatus

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

1. To characterize the behaviour in dry conditions, an air-dried aggregate bed of the control and the three horizons was prepared with five replicates. The series of pressure steps was applied and the changes in bulk density recorded.
2. To characterize the behaviour in a wet state, an identical set of aggregate beds was prepared. The beds were saturated by injecting water under no load until drainage began at the bottom of the samples. The series of pressure steps was then applied while the samples were kept saturated in a free draining state. The changes in bulk density were continuously recorded.

Hydroconsolidation tests

Hydroconsolidation is characterised by an abrupt change in bulk density of samples loaded at their in situ water content and then flooded. Hydroconsolidation under a constant load P_w was studied in a three-stage test:

1. Air-dried samples (5 repetitions for each depth) were loaded step by step to a constant load P_w of 2, 100, 500 and 1,500kPa.
2. While the axial load P_w was maintained on the sample, water was injected at 50mm ³min ^-1 through the porous plate located on the top of the sample until drainage started at the bottom of the porous plate.
3. The load was then increased step by step on the wet samples from P_w to 1,500kPa. Water continued to be added freely at no pressure to keep the sample wet until the end of the test.

Compression-relaxation tests

The purpose of this test was to characterise subsequent 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:

1. Five samples of each horizon were saturated and then loaded step by step to create stresses P_R of 100, 500 and 1,500kPa. Water was added freely at no pressure to keep the samples wet throughout the test.
2. A series of 70 cycles of compression (P_R) and relaxation (0 kPa) was applied on the wet samples. Bulk density was continuously recorded.

Results

Figure 2 presents the compaction curves using the classical compaction approach. Both dry and wet bulk density measurements are presented as a function of axial load. For the pure sand, compaction due to axial load was very low over the range of pressures and there was no significant difference between dry and wet curve (Figure 2-a). Compaction was low and highly heterogeneous between replicates for the three soil samples up to 25kPa. There was no significant difference between the dry and wet samples in this range of pressures (Figure 2-b, c, d). Bulk density increased sharply above 25kPa and became more homogeneous. Beyond 100 kPa, the bulk density increased with depth for any given load all soil samples (Figure 2-b, c, d). At 1,500kPa the dry bulk densities reached 1.60, 1.63 and 1.69 Mg.m^-3 for the 0-15, 15-25 and 40-50cm depths, respectively .

Figure 3 presents the results of the hydro-consolidation test on the pure sand material. The compaction either in the dry or wet state was almost insignificant and there was no significant difference between the dry curve and the wet curve at any pressure. Therefore, the collapse was insignificant.

Figure 2. Air-dried (o) 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

Figure 4 presents the results of the hydroconsolidation test together with the results of the compaction test for the 25-35cm depth layer. Collapse resulting from water injection (represented on the chart as white arrows), always resulted in a final bulk density between the dry and the wet compaction values. The increase in bulk density as a result of hydrocollapse was quite similar over the range 50 <Pw <1,500kPa, even though the largest bulk density change was recorded for an axial load of 100kPa. The bulk density after hydrocollapse was sometimes significantly lower than that of the wet curve (P <0.05). However, the difference was no more significant when the loads were increased after hydrocollapse had occurred. As the dry and wet compaction curves tend to get closer at high pressure, we can assume that for very high loads, no more collapse will occur.

Figure 5 presents the changes in bulk density with increasing water content at constant load (Pw= 1,500 kPa) for the three soil horizons. Two replicates are presented for each depth as a means to highlight heterogeneity. In agreement with the compaction in wet conditions, the lowest collapse was recorded for the 0-15cm depth sample, and the intensity of collapse increased with depth. Collapse always occurred in a range of gravimetric soil moisture between 5 and 15%.

Figure 6 presents the compression-relaxation curves. The bulk density increased by at least 0.1T .m^-3 at P_R=1,500kPa from the initial compaction to the end of rearrangement cycles. The soil samples presented significant elasticity. The material recovered a significant proportion of the porosity when the axial pressure was relaxed but some of the deformation is non-reversible and the bulk density increased for each cycle. The deformation intensity decreased as the number of cycles increased. The rearrangement intensity increased with depth. Similar results were obtain at P_R=100 and 500kPa (data not shown).

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

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

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 and can be considered as being independent of the applied pressure (Figure 4). The sand grains did not reorganize under pressure, even when wet. This result suggests that the lubricant effect of the water was ineffective in the case of this material. Two factors can explain this unusual behaviour. Firstly, the bulk density was already 1.46T m -3 at the beginning of the experiment, probably because the size of the sand grains was distributed over a large range (Table 1). Secondly, most sand grains had a jagged shape according to them aeolian origin, that probably resulted in inter- locking between the grains (Lesturgez, 2005).

Compaction of soil samples

In contrast, the compaction curves recorded with the soil samples in wet condition proved that the same sandy material mixed together with clay and silt was highly compactable. In dry conditions compaction started at around 25kPa and increased with increasing pressure until l,500kPa. In the case of aggregate beds, collapse was in part the consequence of the deformation of the aggregates (Faure, 1976). This process was not active in the pure sand material under study because aggregates were absent. Dry compaction may in part result from the deformation of clay particles. However, the contribution of this process must be limited, given the low clay content of the material (Table 1) and the high proportion of quartz grains within the clay fraction (Bruand et al, 2004). The major contributing factor associated with compaction was probably due to lubrication, the planar-shaped clay minerals helping the sand grains slip against each other.

Hydrocollapse

When water is injected in the samples, hydrocollapse proved to be a phenomenon that developed fully under constant pressure and at any given pressure (Figure 3). Indeed, whatever the initial pressure, the final bulk density was almost identical to the bulk density obtained by compaction in wet conditions. This result, consistent with the observations of Assallay et al. (1998) on loess materials, has a direct application in predicting the collapse. Maximum collapse under any load can indeed be estimated by the difference between the dry and wet compaction curves under the considered load. Maximum hydrocollapse was recorded for P_w=200kPa, close to the value of 100kPa observed by Assouline et al. (1997) on aggregate beds. It has been shown in aeolian deposits that collapse needed a small amount of clay to develop (Rogers et al., 1994), and that collapse intensity increased with clay content up to 25% clay (Assallay et al., 1998). The same increase in hydrocollapse with clay content was observed in this experiment, but the range of clay content covered by the three samples was not sufficient to determine a maximum value. The increase in water content with clay content for hydrocollapse to develop (Figure 5) suggests that the process is related to the hydration of the clay minerals. Faure (1976) mentioned the importance of the clay fraction in compaction of sandy soil and introduced the notion of water potential and clay hydration. In the three horizons hydrocollapse started between 3 and 7% of gravimetric water content. This low water content proves that the phenomenon becomes active in any horizon as soon as it gets wet. The samples presented a mechanical behaviour similar to metastable deposits (Assallay et al., 1997). These properties, usually associated with loess and loess-like deposits (Jefferson et al., 2003), are therefore not confined to silty materials and develop also in sandy soils.

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

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

Compression-relaxation cycles

The mathematical description of soil com­paction is based on relationships between bulk density and applied stress (Assouline, 2002). This approach assumes that after a sample has been consolidated under a pressure P₁, the consolidation would resume only for a pressure P₂ >P₁ (Guérif, 1982). This theory is not applicable to the results of this study as a series of successive stresses under the same axial load resulted in a substantial increase in bulk density (Figure 6). The relaxation between successive stresses allowed the internal friction between sand grains to decrease and therefore permitted the network of forces to reorganise during the next axial load, leading to increased bulk density. The asymptotic shape of the curve showed the development of the soil structure towards the highest possible bulk density. The rearrangement test in a wet state is probably the most representative test to simulate vehicle traffic load as it models as series of confined uniaxial stresses under the same pressure.

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

Contribution of the different processes to total soil compaction

The contribution of dry compaction, hydrocollapse and compression-relaxation cycles to bulk density increase was estimated from our results at a load of 1,500kPa. The last series, namely “field” is the bulk density measured in the field using cylinders (Figure 7). The effect of the three processes on bulk density increased with clay content. However, the contribution of the three processes to bulk density increase remained similar in relative value whatever the clay content. Dry compaction represented around 50% of total compaction, when hydrocollapse and rearrangement ranged between 20 and 30%. In the field dry compaction and hydrocollapse under low pressure (weight of the upper soil horizons) are the first two processes to develop after tillage. The many tillage operations usual in the region induce through a succession of traffic loads, rearranges the fabric to produce the usual massive aspect of the soil with high bulk density. The close lay out of grains, with small particles filling the voids left between bigger ones, has been described by Bruand et al. (2004) as the main factor of high resistance to penetration of the compact layer. Finally, as soil sensitivity to compaction increases with clay content and clay content increases with depth, the most sensitive horizons are the deepest. As a consequence the deeper the soil tillage, the higher is the risk of compaction and the final density. The bulk density is highest in the 20-40cm layer probably because this layer supports the wheels of the tractors during ploughing (at least three times a year). Surface axial load due to vehicle traffic may also be transmitted to subsoil horizons through the massive and often dry topsoil, increasing bulk density through rearrangement processes. In the field the highest bulk density values were recorded in the 20-40 cm (Figure 7) depth interval despite the higher sensitivity to compaction of the lower horizon (Figure 2). Two kinds of tillage operations are to distinguish: frequent tillage of the 0-20 cm interval depth and some punctual deep tillage operations with the objective to break the compact layer. As the soil is highly collapsible and sensitive to rearrangement, the density of the post-tilled layer reach inevitably high values as a function of time. The frequency of tillage in the topsoil (0-20cm) does not allow high density as in the 20-40cm interval depth as the structure return frequently to the tilled state. However, the 20-40cm interval depth benefits as it has the enough time to accumulate the combine effect of the traffic load. As for the lower layers (>40 cm depth), tillage operation have never change organisation of the structure and if aggregates beds from this layer are highly sensitive, the actual weakly developed structure is stable. It has been shown that tilled layers are much more sensitive to compaction than massively structured or already compacted subsoil (Schäfer-Landefeld et al., 2004). Porosity of this layer is mainly constituted of biopores which are usually stable because they develop in a stable structure (Dexter, 1987; Bruand et al., 1996). These results suggest that the deeper the soil is tilled, the higher is the risk in obtaining high bulk densities. Deep tillage is therefore not an option to rehabilitate compact subsoils due to the instability of the resulting structure. However, alternative techniques such as slotting (Hartmann et al., 1999) or biological drilling (Lesturgez et al., 2004) have proved to be efficient is such unstable soils. These techniques ensure the development of pathway for the roots through the compact layer and preserve the massive and stable structure surrounding them.

Figure 7. Dry compaction, hydroconsolidation and rearrangement (compression-relaxation cycles for each depth at Pw = 1,500 kPa

Conclusions

The compaction of the sandy material studied under uniaxial load was trivial, even in wet conditions. The same material was highly sensitive to compaction when mixed with silt and clay. The sensitivity to compaction increased with increasing clay content. Compaction in the dry state, hydrocollapse (collapse under increasing water content at constant pressure) and rearrangement under a series of successive loads were more pronounced when clay content increased. However, the contribution of each phenomenon to final bulk density was approximately constant whatever the clay content. Most part of soil compaction (around 50%) was due to dry compaction. Hydrocollapse explained about half of the remaining compaction. Hydrocollapse was responsible for sharp increases in bulk density as a result of small increases in water content (gravimetric water content between 3 and 7%), even under low pressure. The rearrangement under successive loads explained 20 to 30% of the final bulk density, even though the bulk density was already higher than 1.65Mgm ^-3 after dry compaction and hydrocollapse. As clay content increased with depth, the deeper horizons were the most sensitive to compaction. The highest bulk densities were however measured in the 20-40cm layer in the field. The direct traffic load resulting from the many ploughings a year usual in the region is probably a part of the explanation but the structural effect of deep ploughing (which changed the massive structure of the layer into a metastable organisation of aggregates very sensitive to densification) is probably the main factor. Deep tillage is therefore not an option to rehabilitate compact subsoils due to the instability of the resulting structure and alternative techniques conserving part of the initial stability are recommended.

Acknowledgments

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

References

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Hartmann, C, Poss, R., Janeau, J.L., Bourdon, E., Lesturgez, G. and Ratana-Anupap, S., 2002. Use of the granular material theory to interpret structural changes in a sandy soil. 17^th World Congress of Soil Science, Bangkok, Thailand.

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¹ IRD, UR176 SOLUTIONS, Land Development Department, Office of Science for Land Development, Phaholyothin Road, Chatuchak, Bangkok 10900, Thailand, [email protected]
² INRA, Unité de Science du Sol, Centre de Recherche de Versailles-Grignon, Route de St-Cyr, 78026 Versailles, France.

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

Introduction

Sandy soils are very unstable or evolving materials, whose properties are not well known, making it thus difficult to manage for agricultural purposes. Due to the low content of clay, the cohesion between grains of the soil is low and the sandy soil can be particularly sensitive to any external perturbation, whatever the origins are: climatic (intense rain, capillary rise) or anthropogenic (ploughing, mechanical vibrations) for example. In this work, we are considering the sandy soil as an example of fragile matter from a physical point of view; our approaches are to identify the most simple elementary mechanisms responsible for the instability and the reorganization of the sandy structure and thus to characterize the physical parameters involved in the weakness of this type of soil. We thus use a very simple model of granular soil without any biological or chemical influences. This approach aims to test the part of the physical influence in the instability of real soils.

In a first section, we will describe how we reduce the problem to model physical experiments and mention the characteristic features of dry granular media. In the second section we will describe in more details a particular experiment for testing the instability of a granular media. In particular the resistance to reorganisation of a granular medium is characterised by the ability of an intruder to move in it. The strength     needed to displace it and the size of the reorganisation around critically depends on the original packing of grains and could give information on the ability of a worm or a root to penetrate this type of medium.

I – Model granular media for experiments

Granular matter we use in physics are collections of grains of controlled dispersity, simple form and known grain density (Fontainebleau sand made of rounded grains of 300 µm of diameters, monodisperse glass beads or metallic ball-bearing beads…). Their diameters are always larger than the micrometer, so that the thermal agitation does not play any role in the motion of the grains. Moreover, we choose large diameters (of the order of 100 µm to several millimetric sizes) to minimize for example drag forces produced by the interstitial fluid (generally air in the porosity of the granular network) so that the interactions are mediated through the direct contacts between grains. In the case of non-cohesive grains, these interactions are limited to collisions and contact forces, according to the duration of contact between grains.

Despite these drastic simplifications which seem to be very naive from a practical point of view, the variety of phenomena observed with model granular media is very rich and still complex. We will describe below the main features of a granular structure which could play a role in a real sandy soil.

The heterogeneity of forces

In granular materials, force is rarely transmitted uniformly, but rather preferentially along a network forming force chains. The network of contact forces can be observed by photoelastic measurements (Figure 1) (Behringer). It appears to be very heterogeneous, forming chains along which the forces are particularly intense encompassing regions bearing relatively small loads. Then the description of the transmission of forces inside a granular medium is quite a great challenge where the inhomogeneity of the material leads to unexpected behaviours.

Figure 1. Force distribution network as observed in a photoelastic system with birefringent discs placed in between circular polarizers (Behringer)

The spatial distribution of forces is large, with fluctuations of the order of the mean force. According to (Radjai et al., 1997) the network of contact forces can be divided into 2 parts: the large network for forces larger than the mean force bears most of the load with a stress tensor and angular distribution of contact directions which is suited to oppose external constraints. On the other hand, the small force network (forces smaller than the mean force) shows isotropic contact direction and a weak anisotropy of the stress tensor with the major principal axis oriented in such a way that it opposes the buckling of large force chains (Clément, 1999).

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

The history dependence

The protocol of preparation is particularly important for granular materials and determines the subsequent mechanical properties. For example preparing a dry sand pile by using a point source (sand falling from a funnel) or a pluviation technique (sand falling from a grid) leads to the same macroscopic pile with a repose angle (angle between the slope of the pile and the horizontal) which is around 30° for both piles (Figure 2). However the measured pressure profiles on the bottom below the sand piles are rather different. When the sand pile is built from a point source, there is a dip of pressure below the apex of the pile, while there is a maximum of pressure when the pile is prepared by pluviation (Vanel et al., 1999). This drastic difference in the pressure profiles can not be inferred from macroscopic properties like the angle of repose and therefore the internal coefficient of friction is not sufficient for describing the mechanical properties of a sand pile. Some microscopic parameters have to be taken into account.

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

The importance of preparation can act on packing fraction but also on finer parameters like the directions of contacts between grains and the orientations of the force network (De Gennes et al., 1999). The evolving nature of the mechanical properties of a granular medium can be illustrated by the following experiment (Figure 3) where some photoelastic discs are placed into a shear box. Initially before applying the shear the medium is isotropic (there is no anisotropy in the orientations of contact directions) and the response to a point force on top of the box is maximal along the direction of the force (applying a point force is a way to test the mechanical properties). However if the box is submitted to an nitial preshear some new force chains are created along direction 1 which tend to oppose the shear. A new “texture” is formed and the mechanical properties have changed, as it can be observed on the shift of the response to a point force (Atman et al., 2005).

Figure 3. Importance of the microscopic scale on the mechanical properties
Left: schematic of the shear box.
Middle: Visualisation of contact forces between grains by use of photoelastic grains.
Right: Mean response to a point force applied along the direction of the arrow. The intensity of the mean stress grows when it is darker (Atman et al. 2005).

The fragility

Granular materials as other particulate materials are examples of fragile matter. For non-cohesive grains there is a lack of resistance of contact forces to any extension. The internal structure (the contact and force networks) can evolve and adapts itself to support the applied load as we have seen before. Then the incremental response can be elastic only to “compatible” loads. Incompatible loads like the one produced for example by a change of compression axis, even if small, will cause finite, plastic reorganizations: irreversible rearrangements will be produced in the structure (Cates et al., 1998).

The different scales

The approach used at a macroscopic scale in soil mechanics is usually based on standard compression experiments like triaxial tests, from which constitutive relations between stresses, deformations and directions of deformations are obtained. In this approach, the soil can be considered as an effective continuum medium but the constitutive elasto-plastic relations between stresses and strains inferred from these tests are mostly non-linear, piece-wise, anisotropic and crucially depend on the history of the loading/unloading cycles (Clément, 1999).

The problem of granular materials is that there is no clear separation between microscopic and macroscopic scales, from the size of the micrometric asperities in the surface area of contact of grains to the mesoscopic scale of force chains and till the macroscopic size of the bulk material of soil. Therefore many scales are involved in the resulting mechanical properties and microscopic rearrangements can have a drastic effect on macroscopic properties. This is the reason why we perform the following experiment.

II – Experiment on reorganizations in a granular medium due to a solid intrusion

In this part we describe in more details a conceptually simple experiment (Kolb et al., 2004). It consists in testing the local resistance of a granular material by moving an intruder in it. From a practical point of view it bears similarities with standard penetrometry tests currently used in soil mechanics.

However we want to focus here on the microscopic perturbation introduced by the measurement itself, which is a consequence of the fragile nature of granular material. The network of contacts between grains is not permanent and the perturbation induced by the motion of an intruder (which can be a rough model for the growth of a root or the progression of a worm) can open or close some contacts and produce some irreversible rearrangements that change the nature of the granular structure itself and thus of the complementary porous matrix, what affects its mechanical properties at a larger scale. Therefore we want to characterize the rearrangements induced by the displacement of the intruder and the range of the effect of perturbation inside the granular material. Thus we apply a local and cyclic perturbation inside the granular packing for both detecting the displacements of grains in the vicinity of the perturbation and characterizing the evolution of the structure by investigating the irreversible displacements after a given number of cycles of perturbation.

Experimental setup

For this purpose we use a 2 dimensional (2D) granular media. That means the motions of grains can only occur inside a plane, there is no influence of the third dimension. Once again it is an oversimplification of a real sandy soil but it gives some hints on the micro-reorganizations of granular material because the 2D geometry allows to directly follow the motion of each grain by simply using a camera above the setup. More precisely the grains are not beads but small metallic hollow cylinders whose form is adapted to the 2D geometry: the axis of the cylinders are perpendicular to the plane of motion (see Figure 4 right part) The cylinders have two different outer diameters d₁ = 4 mm and d₂ = 5 mm. Mixing 2 types of grains leads to a disordered granular media by avoiding crystallization, i.e. regular stacking of the grains. This is done in purpose for obtaining generic results. The inner diameters of the cylinders are also different, which allows a proper determination of the type of grains for further image analysis.

Figure 4. Left: Experimental setup. Right: typical frame of observation of the piling. The intruder is below the black point (inset: sketch of the experimental setup viewed from the side)

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

For the experiment the bottom plane is tilted at an angle 0 (see Figure 4 inset of the right part) such as to control the confinement pressure inside the granular material by an effective gravity field gsin 0 where g is the gravity acceleration. A value of 0 = 33° is chosen for being larger than the static Coulomb angle of friction between the grains and the glass plate which is around θ = 20° (µ_grain/glass = tan θ is the static friction coefficient between grains and glass). Therefore the grains spontaneously move downward if they have the possibility to find a place below.

The intruder is a big grain of diameter d₂ located in the median part of the container at a 21.2 cm (i.e. 42 d₂) depth from the upper free surface. The intruder is attached to a rigid arm in Plexiglas (reinforced by metallic parts) moved by a translation stage and a stepping motor driven by a computer. The arm motion takes place along the median axis Y of the container and is parallel to the plane. In this report we use an intruder displacement value U₀ of a fraction of a grain diameter (U₀ = 1.25 mm ≈ d₂ /3) giving a typical strain less than 10^-2, far above the elastic limit but also far below the usual fully developed plasticity domain where shear bands appear. The intruder is moving up then down to its first position and then again up and down and so on with always the same amplitude of displacement U₀, thus performing cycles of displacements in a quasi-static way. The up and down motions along the Y-axis are separated by rest periods during which pictures with a high resolution CCD camera (1280*1024 pixels²) are taken. The image frame is centered slightly above the intruder and covers a zone of area 39 d₂*31 d₂ (see Figure 4 right part).

In the following, we use the notation i for the index corresponding to the i^th image just before the i^th displacement of the intruder (upward or downward) and n for the cycle number with n = int[{i+1}/2] where int is the integer part. For each image i, the center of each grain is determined with precision using the computation of the correlation on grey-levels between an image of the packing and two reference images corresponding to both grain types (d₁ and d₂). Note that the inner diameter of the cylindrical hole, which is different for each grain type (small or big), helps crucially for the proper determination of the centre and of the grain type. Hence, we obtain, for each image, the locations of more than a thousand grains with a resolution down to 0.05 pixels. The displacement of each single grain is then calculated by the difference between its position in image i and in image j. This method allows a precision of less than 10 µm (d₂ /600) for the displacements. Thus we obtain 2 types of informations:

• the displacement field in response to an upward or downward intruder motion (also called the response function) by comparing images i and i+1.
• the irreversible displacement field by comparing images i and i+2. (Between images i and i+2 the intruder has accomplished a cycle of displacement but some grains don’t come back to their first positions; they have undergone irreversible displacements).

Experimental results

Displacement fields as a response to the motion of the intruder

The displacements fields have been computed for 16 independent realizations prepared in the same way. We plot in Figure 5 the displacement of grains induced by an upward motion of the intruder (the figure presents the response obtained in the case of the second upward motion of the intruder, for example). We observe that the amplitudes of displacements are very small and that there is some redirection effect towards the lateral walls, but the most important point is that the grains that move are not obligatory close to the intruder and that the perturbation due to the solid intruder has a long range effect. The second point is that the displacement field is very sensitive to the particular organization of grains and probably linked to the force network of each configuration.

Figure 5. Displacements fields observed for the second upward motion of the intruder (i = 3 or n = 2) for two independent realizations a and b. The point corresponds to the location of the intruder. All displacements have been magnified by a factor of 50 and the scales are given in pixels. The intruder is initially located in X= 0, Y= 0 before its upward motion

We can extract from these results a mean behaviour by averaging over the 16 realizations inside little binning cells of size 1.2 d₂*1.2 d₂ regularly located in the Cartesian coordinates (O, X, Y) reference frame.

Figure 6. Mean upward displacement field for the second upward motion of the intruder (( = 3or« = 2). All displacements have been magnified by a factor of 70. The coordinates are expressed in unity of a big grain size d₂

This gives the mean displacement field presented in Figure 6. We clearly notice that the granular motion is not localized in the vicinity of the intruder and that this small perturbation of only one third of a grain diameter indeed produces a far field effect. Furthermore, the presence of two displacement rolls is observed near the intruder. They are located symmetrically on each side of the intruder but turn in opposite directions. Besides this near field effect, the main response principally occurs above the intruder with displacement vectors that tend to align along the radial directions from the intruder.

The typical decay of the response with the radial distance r from the intruder is analysed. After several cycles the response to an upward perturbation exhibits a 1/r^a dependence where a is close to 1, what can be modelled by the following relation (eq.l):

This relation is valid in the upper part above the intruder for a distance larger than 7 d₂ (far enough from the rolls). The function / (6) of the polar angle 6 (defined in Figure 4) has a typical bell shape with its maximum value for 6=0 corresponding to the direction of the intruder motion. The dimensionless parameter b_t gives the amplitude of the response for the i'^h intruder motion.

Evolution of the response with the number of cycles: reversibilty/irreverdibilitu

We followed the evolution of the response (via the parameter b_t ) with the number of cycles or equivalently with i: the parameter b_i decreases progressively with i and then saturates to a constant value after about 60 displacements, i.e. 30 cycles. Each cycle of motion of the intruder produces some irreversible displacements of grains, and then the structure of the material changes and the following response to the next motion of the intruder is different. Note that in spite of these irreversible displacements mainly downward in the direction of gravity, there is no detectable increase of the mean packing fraction (averaged over the 16 experiments) with the number of cycles n: it stays constant with a relative error of 0.1%. But after n ≈ 30 cycles, both mean responses for upward and downward motions of the intruder are almost identical: a quasi-stationary regime or “limit cycle’’ is obtained and the packing seems to be more stable with regard to the perturbation.

Figure 7. Mean upward displacement field for normal (above) and tapping (below) preparations for the 9^th cycle. The grey-level code corresponds to different amplitude of displacements given in pixels. 33 pixels correspond to the diameter of a big grain d₂

Dependence on preparation

We now compare 2 modes of preparation: the original one obtained by random initial mixing of grains inside a specific surface and the so called “tapping one’’ consisting in tapping the walls of the inclined container just before beginning the experiment. Note that the initial mean packing fraction is c = 0.750 ±0.002 for tapping preparation so that there is no significant change of ø compared with the first preparation described before (called the normal one).

However the effects on the subsequent response observed by mean of the displacement field are quite visible as it can be observed on Figure 7 with grey-levels corresponding to different amplitudes of displacements. We clearly observe that the response is enhanced and more directive in the direction of gravity for the tapping preparation. In both cases, changes in mean packing fraction along the experiments are less than 1/1,000 and they certainly would not explain such differences in the evolution process. It is then natural to look for the influence of local configuration parameters such as the evolution of contact direction distribution or other texture parameters at the level of the grains. This analysis reveals that a difference could be observed between the 2 types of preparation only if we compare the mean coordination number (the mean number of contacts per grain), which is a microscopic parameter at the level of the contact size.

Conclusion

We experimentally determine the reorganisation field due to a small localised cyclic displacement applied to a packing of hard grains under gravity modelling the physical parameters that could be involved in a sandy soil. We surprisingly find that the displacement fields in response to the small local perturbation are quite long range in the direction of the perturbation and quite evolving. We also propose here new results on the effect of a slight difference in the preparation procedure: We compare the evolution of the response function along the cycling procedure and we show that the initial configurations prepared either by random mixing of grains at constant surface or under a weak tapping have a clearly different response even though the mean packing fraction obtained in these two cases are extremely close. Not only the first response but also the further evolution during the cycling procedure is different, showing that there is still a memory effect of the initial preparation after many cycles. With this experiment we want to emphasize the role of microscopic rearrangements in the stability of a granular packing.

References

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

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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.

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¹ ESPCI/UPMC, PMMH (Laboratoire de Physique et Mécanique des Milieux Hétérogènes), Equipe Granulaires, 10 rue Vauquelin, 75231 Paris Cédex 05 France, kolb@ ccr.jussieu.fr
² ENS, LPS, 24 rue Lhomond, 75 005 Paris, France