The essential mechanics of capillary crumbling of
structured agricultural soils
O.B. Aluko
*, A.J. Koolen
Soil Technology Group, Wageningen University, Bomenweg 4, 6703HD Wageningen, Netherlands
Received 5 July 1999; received in revised form 28 January 2000; accepted 17 February 2000
Abstract
In soil loosening processes like seedbed preparation, signi®cant soil crumbling is often desired. A better understanding of the mechanics of crumbling is necessary to optimize crumbling operations, particularly in structured agricultural soils in which capillary bonds are dominant. To this end, a model of the mechanics of capillary crumbling in structured agricultural soils is developed. Four sets of experiments on cylindrical soil samples were carried out to investigate the validity of the model and soil crumbling characteristics as in¯uenced by freezing, thawing and drying. After preparation and sample pre-treatment, the samples were dried to different moisture contents and then tested to determine soil bonding strength. Soil water suction was also monitored at testing as were sample dimensions at different stages of experimentation. The model was found to account satisfactorily for the mechanics of capillary crumbling in structured agricultural soils. Freezing had the effect of reducing the strength of inter-aggregate bonds whilst preserving the integrity of soil aggregates during crumbling.
#2000 Elsevier Science B.V. All rights reserved.
Keywords:Soil bonding strength; Soil structure; Capillary bonds; Soil moisture content; Mechanics of crumbling
1. Introduction
When such assessments as traf®cability, water in®ltrability and workability of an agricultural soil are desired for cultivation and agricultural production purposes, two physical properties are of primary importance: soil textural composition and soil struc-ture. The textural composition of a soil is largely ®xed with possible but minor changes being made in the organic matter content. Soil structure, on the
other hand, is a transient property which can be altered by different processes. Such processes include shrinking and swelling, drying and wetting, freezing and thawing, human, animal and vehicular traf®c, mechanical tillage operations and incorporation of organic matter.
The importance of soil structure cannot be over-emphasized. For example, the state of the soil struc-ture can be a farmer's greatest asset or his greatest risk. The integrity of aggregates, the type and strength of aggregate bonds, the size and distribution of pore spaces within the soil and the moisture content are salient factors that determine the state of structure of an agricultural soil. When aggregate bonding is the decisive factor, Koolen and Kuipers (1989) have suggested that a soil consisting of ®rm units
*Corresponding author. Present address: Department of
Agri-cultural Engineering, Obafemi Awolowo University, Ile-Ife, Nigeria. Tel.:234-362-30290; fax:234-362-32041.
E-mail address: oaluko@oauife.edu.ng (O.B. Aluko)
(aggregates) with relatively little bonding between adjacent aggregates at the mutual points (or areas) of contact, can be regarded as having a good structure. The phenomenon of ``crumbling'' in agricultural soils is very important in the development of soil structure. Indeed, agricultural soils can be regarded as having a crumb structure (Russell, 1973). This crumb structure approach has been used by Chandler (1985) to explain the crumbling of agricultural soils as a fracture process which involves the breaking of bonds between soil crumbs (or aggregates). When the crumbs are hard and the bonding between crumbs is weak, the soil cracks in a brittle manner. On the other hand, when the bonding between the crumbs is strong compared with its internal strength, it may become distorted without breaking (i.e. it is ductile). Snyder and Miller (1989) also attributed crumbling in agricultural soils during tillage operations, to failure by cracking due to tensile stresses. For struc-tured agricultural soils where capillary bonds play a dominant role, Koolen (1987) proposed a capillary bonding stress, pw (N/cm2), which is a function of
the soil water suction and the degree of pore satura-tion.
This paper reports an experimental-analytical investigation to examine the mechanics of capillary crumbling in a structured agricultural soil. In parti-cular, Koolen's model of capillary bonding was further developed and the effects of freezing, thawing and drying on crumbling as well as the integrity of soil structure, were studied.
2. Theory
In general, soil strength is derived from two sources: inter-aggregate bonds and intra-aggregate bonds. The strength of a soil is a re¯ection of the force required to break these bonds. Fig. 1 is a physical model of two aggregates in a structured soil, hatched vertically and horizontally, respectively, that are in contact at positions 1, 2 and 3 in plane I. The pores between the aggregates are relatively larger than those within the aggregates. At contact positions 1, 2, and 3 the tension in the soil water ``clenches'' the particles together. Based on this clenching force, Koolen (1987) considered surface-elements within the soil such as planes I and II and derived a capillary bonding force
per unit area (i.e. capillary bonding stress), pw (N/
cm2), given by
pwuS (1)
where u is the soil water pressure (i.e. soil water suction in units of stress) andSis the degree of pore saturation, which is the fraction of the total pore volume within the bulk soil occupied by water. The range ofS is 0±1.
In a further analysis of Eq. (1) (see Fig. 2), Koolen considered its implications in a structured clay soil with inter-aggregate pore spaces that fall within one narrow size class. He reasoned that as the soil dries out from an initially wet state, the trend in the capillary bonding stress (pw) within aggregates would differ Fig. 1. Physical model of the contact zone between two aggregates in a structured soil (after Koolen, 1987): pw, capillary bonding
stress;u, soil water suction;S, degree of pore saturation.
Fig. 2. Thepw±u±Sdiagram of capillary crumbling proposed by
from that between aggregates. Thus in Fig. 2, curves A and C illustrate the pF (logu) curve (whereuis expressed as a negative pressure head in cm water column) and the trend ofpwwithin aggregates,
respec-tively, while curves B and D describe the pF curve and the trend ofpwbetween aggregates, respectively.
The horizontal portion of curve B refers to the empty-ing of inter-aggregate pores within a particular size class with little or no increase in soil water suction.
Koolen's model suggests that, corresponding to this emptying, the capillary bonding stress between aggre-gates decreases (see curve D) and then begins to rise again as soil water suction again increases.
In an investigation into the mechanics of cracking of remoulded clay bars, Towner (1987) stated that the tensile strength of a soil is a material property that depends in general on both the soil water suction and the water content. In another study of the tensile strength of unsaturated soils, Snyder and Miller (1985) used a modi®ed effective stress equation to estimate tensile strength, st. Their equation can be
expressed in the form (Snyder and Miller, 1989):
st ÿw yuw (2)
where the factorw(y) is a function of the degree of pore saturation of the soil anduwis the negative hydrostatic
pore water pressure. It is interesting to note that the terms on the right-hand side of Eq. (2) are similar to those in Eq. (1). Now, Mullins and Panayiotopolous (1984) have pointed out that in structured soils, only the fraction of water in the inter-aggregate pore space will contribute to the cohesion between adjacent aggregates which ultimately determines the strength of a structured soil. In view of this, Snyder and Miller (1989) suggested that the use of an ``effective'' degree of pore saturation, ``ye'', based only on the
inter-aggregate porosity of soil, might give a better estimate of the tensile strength of soil in Eq. (2).
Assuming that the foregoing arguments are valid, an expression, similar to Eq. (1), can be written for the soil tensile strengthst (N/cm2) as follows:
stuSi (3)
whereSiis the degree of inter-aggregate pore
satura-tion, which is de®ned as the fraction of the inter-aggregate pore space occupied by water. Like S, Si
ranges from 0 to 1.
In conjunction with Koolen'spw±u±Sdiagram (see
Fig. 2), Eqs. (1) and (3) constitute the proposed capillary crumbling model for structured agricultural soils in which capillary bonds are decisive. In com-parison withst,pwis an index of the bonding strength
of the bulk soil whereasstis an index of the bonding
strength at inter-aggregate locations. Series of experi-ments, in which soil tensile strength, soil water suction and degree of pore saturation were measured, were carried out to investigate the validity of the proposed capillary crumbling model. The materials used and experimental procedure will now be described.
3. Experimental work
3.1. Soil preparation
The soil used for this investigation was a Wagenin-gen silty clay loam (36% of minerals <2mm, 2.3% of soil is humus, water content at pF 2 is 0.27 g/g, CaCO3
content is 3.3%, pHKCl is 7.4), a full description of
which is given by Koolen (1972). Natural (undis-turbed) top soil was carefully collected from an arable layer (0±200 mm) and frozen in trays, at a temperature of ÿ188C, for a period of 72 h. The soil was then allowed to air-dry to a moisture content of 0.1747 g/g in order to allow mechanical sieving without internal destruction of aggregates. In the course of this inves-tigation, soil moisture contents were determined by the gravimetric method. The size fraction between 0.6 and 5.0 mm was then obtained by mechanical sieving. This was allowed to equilibrate for 48 h in a sealed plastic container. The soil was then moistened to a moisture content of 0.27 g/g, using water spray jets, and subsequently allowed to equilibrate for 24 h in sealed plastic containers.
Immediately after preparation, each sample (still inside the core sampler) was placed and wrapped in a sealed, transparent plastic bag and then subjected to further treatment(s) prior to testing.
3.2. Tests and measurements
On the basis of sample treatment(s) prior to tensile strength testing, four different sets of experiments were carried out. These have been coded EI, EII, EIII and EIV, respectively. These sample treatments con-sisted of equilibration prior to freezing (in sealed, transparent plastic bags) for 24 h, freezing at a tem-perature of ÿ188C for 24 h (EI, EII and EIII only), thawing for 24 h (EI, EII and EIII only), drying by passing a warm air stream through the sample for selected periods (minutes and/or hours), equilibration after drying (for 24 h) in sealed, transparent plastic bags and then tensile strength testing. Thus, only samples of experiment set EIV were not subjected to the freezing and thawing pre-treatments prior to drying.
The conduct of an experiment set entailed the drying of each sample to a progressively lower soil moisture content than the preceding sample. There-fore, only one sample was tested at each moisture content within a particular experiment set. Experiment sets EI, EII and EIII are replicates of the same investigation, carried out primarily for reasons other than statistical reasons. Experiment set EII replicates EI with a very important difference: the average drying interval between successive tensile strength tests is reduced. Experiment set EIII was carried out for further veri®cation of the results obtained in EII. Thus, in these replicates (EI, EII and EIII), the emphasis is on the trends over approximately the same range of soil moisture content and not on the replication of tests at speci®c, individual moisture contents.
After drying and subsequent equilibration, the dia-meter and height of each sample, as illustrated in Fig. 3(b) and (c), were measured before further testing to determine its tensile strength. This was accom-plished using a pair of vernier calipers. Soil tensile strength was determined by subjecting each sample to the Brazilian test. The Brazilian test consists of dia-metrically loading a cylindrical soil sample until it fails in tension as shown in Fig. 3(d). The applied load,
F(N), and the strain during testing were recorded and later used to determine the tensile strength,st(N/cm2),
of the soil. Several of these tests were carried out on soil samples at different moisture contents using a tension and compression-testing machine. The soil water suction,u(mbar), of the sample was measured immediately after the Brazilian test by inserting a small tensiometer needle to prevent undue sample disturbance. The tensiometer needle had a diameter of 2 mm. One measurement per sample was suf®cient because the water tension in such samples is very uniform. The tensiometer itself used a very small stress-transducer and the highest water tension value that was measured was 830 mbar. The sample
Fig. 3. Typical sample particulars at different stages of experi-mentation viz. (a) original dimensions at preparation; (b) and (c) dimensions after drying; (d) particulars at failure in the Brazilian test: H0, sample height at preparation; h1, sample height after
drying;Dh, change in sample height (h1ÿh0);D0, sample diameter
at preparation; D1, sample diameter after drying; Df, sample
diameter at failure;DD, change in sample diameter (D1ÿDf);F,
moisture content at testing was then determined by the gravimetric method.
For each experiment set, values of capillary bond-ing stresspw(N/cm2) were calculated using Eq. (1).
Sample dimensions and loading forceF(N) at failure, recorded prior to and during Brazilian tests respec-tively (see Fig. 3(d)), were used to estimate tensile strength st (N/cm2) according to the relationship
(Kirkham et al., 1959):
st 2F pD1h1
(4)
whereh1(cm) andD1(cm) are the sample height and
diameter, respectively, after drying. Values ofSiwere
subsequently calculated using Eq. (3). The diametric strain-to-failure (eD) during the Brazilian test was also
determined as follows:
eD
D1ÿDf
D1
DD
D1
(5)
whereDf(cm) is the sample diameter at failure. An
estimate of the size of pores being emptied during drying, can be obtained by considering the capillary rise relationship
u0:15 cosa
r (6)
wherer(mm) is the radius of the capillary anda(8) the contact angle of water. Assuming that complete wet-ting takes place (i.e. a08) then Eq. (6) can be expressed as
2r0:30
u (7)
Eq. (7) has been used in the literature (Kutilek and Nielsen, 1994), and is used in this study to estimate the equivalent diameter of pores (2r) being emptied at different soil water suctions.
4. Results and discussion
4.1. Effect of moisture content and drying interval on bonding strengths
The capillary bonding stress (pw) and the measured
tensile strength (st) are plotted over a range of
moist-ure content in Fig. 4(a) for the ®rst set of experiments,
EI. As the soil dries out, both pw and st initially
increase. This is in agreement with Causarano (1993), who showed that tensile strength of aggregates depends mainly on water content. It appears that st
increases at a continuously increasing rate as the soil dries out. The recorded increase instin the relatively
drier moisture range (between 0.20 and 0.15 g/g) is more than double the increase in the wetter moisture range (between 0.25 and 0.20 g/g). The trend ofpwon
the other hand, shows little or no increase in the drier moisture range (0.20±0.15 g/g), its increase being almost entirely limited to the wetter moisture range (0.25±0.20 g/g). The ®gure also shows that the values ofstare generally lower than the corresponding values
of pw. This is in agreement with Panayiotopoulos Fig. 4. Bonding strength plotted against soil moisture content for experiment sets EI (a) and EII (b):pw, capillary bonding stress;st,
(1996) who reported that theoretical tensile strength values (calculated with a formula similar to Eq. (1)) were 10 or more times greater than measured values. According to the present theory, in the wetter moisture range especially when the degree of pore saturationS
is near 1, it is expected that both pw and st should
approach the same value because both S and Si
approach the value 1. At a moisture content of 0.2482 g/g in Fig. 4(a) however,pwis approximately
three times the value ofst. This suggests that
appreci-able emptying of inter-aggregate pores had already taken place between the initial moisture content of 0.27 g/g and the moisture content 0.2482 g/g at testing, rendering Si at 0.2482 g/g moisture content much
lower than S.
The trends ofpwandstare plotted as a function of
the equivalent pore size (diameter) being emptied in Fig. 5(a). It can be seen that bothpwandstincrease
with decreasing pore size. In Figs. 4(a) and 5(a), there is no evidence of the expected fall in tensile strength which, as predicted by the theory, should coincide with the emptying of pores of a certain size class at an approximately constant soil water suction. On close examination, it appears that the relatively large drying interval between successive tests in experiment set EI, might have had an obscuring effect on this phenom-enon. These observations, whilst precluding a satis-factory analysis of the pw±u±S diagram from these
initial results, informed the decisions to begin sample testing at higher initial moisture contents (i.e.Scloser to 1) and reduce the average drying interval between successive tests in the conduct of subsequent experi-ment sets.
Fig. 4(b) shows the values ofpwandstfor
experi-ment set EII plotted as a function of moisture content. As drying proceeds, both st and pw increase in a
manner similar to that shown in Fig. 4(a). As discussed earlier, the capillary crumbling model postulates thatstpwat all times and that the conditionstpw
occurs whenSiS1. It is therefore interesting to note
that in Fig. 4(a) and (b), the magnitude ofstis always
lower than that of pw. Furthermore, at a moisture
content of 0.2866 g/g (see Fig. 4(b)), which corre-sponds to a degree of pore saturationSof 0.899, the
values of pw and st are almost the same Ð the
difference being of a negligible order of magnitude. These results indicate that non-capillary bonds were not involved in soil crumbling and that capillary bonds
indeed constituted the dominant bonding force in this soil.
4.2. The capillary crumbling model
The fall in tensile strength, predicted by the theory, appears to have occurred in Fig. 4(b) in the narrow moisture range between 0.2261 and 0.2240 g/g. The size range (i.e. equivalent pore diameter) of inter-aggregate pore spaces emptied within this narrow moisture range is 5.56±6.00mm (see Fig. 5(b)). The range of soil water suction at which these pores were emptied is 500±540 mbar.
Fig. 5. Bonding strength plotted against equivalent pore diameter for experiment sets EI (a) and EII (b):pw, capillary bonding stress;
The pw±u±S diagram for experiment sets EII and
EIII are shown in Fig. 6(a) and (b), respectively. The general forms of curves A, B, C and D in Fig. 2 can be recognized in the trends for S, Si, pw and st data,
respectively, in both diagrams. Pertaining to a dec-rease in bonding strength, two observations are evi-dent. Firstly, the fall in bonding strength is re¯ected not only in the trend forstbut also in that forpw. In
Fig. 6(a) and (b), the data points in the region where this phenomenon occurred have been encircled
for emphasis. This observation is better appreciated by carrying out a closer examination of these data points. The encircled data points of Fig. 6(a) are therefore shown blown-up in Fig. 7 with lines and arrows included to show the actual path of succession between the data points. Secondly, the fall in tensile strength is not as pronounced as that predicted by the theory (see curve D of Fig. 2). This apparent differ-ence between the theory and the experimental results can be explained by considering the distribution and
Fig. 6. Experimentally determinedpw±u±Sdiagrams for Wageningen silty clay loam (a) EII and (b) EIII:pw, capillary bonding stress;st, soil
relative proportion of inter-aggregate pores of differ-ent sizes. The condition for curve D in Fig. 2 is that inter-aggregate pores of a particular size class must occur in a relatively overwhelming proportion within the soil. Conversely, when inter-aggregate pores of different sizes are uniformly distributed within a soil, the fall in tensile strength illustrated in curve D in Fig. 2 will disappear. The results illustrated in Fig. 6(a) and (b) indicate that such inter-aggregate pores of a particular size class, did occur in appreciable but not overwhelming proportion within the soil tested. As mentioned earlier, the size class of these pores in experiment set EII, for example, is given by the equivalent pore diameter range 5.56±6.00mm.
When compared with curve A in Fig. 2, the trend of
Sdata with increasing soil water suctionuin Fig. 6(a) and (b), is consistent with what is expected. A de®nite trend can also be seen in the plottedSidata as the soil
water suctionuincreases. Bearing in mind that inter-aggregate pores of a particular size class did not occur in overwhelming proportion as explained above, this trend compares reasonably well with curve B in Fig. 2. However, at the highest levels ofu(720 and 830 mbar in Fig. 6(a) and (b), respectively),Siseems to increase
Ð a deviation from the general trend. Considering that
Sidata are calculated from measured values ofstand u, a possible explanation for this apparent deviation is that the measured values of u at those levels were inaccurate. This means that relatively high levels of soil water suction (u720 mbar) are dif®cult to mea-sure accurately using a small tensiometer.
4.3. Effect of freezing on bonding strengths
The effects of freezing on the capillary bonding strengths pw and st are illustrated in Fig. 8. In the
®gure,pwandstdata for experiment sets EII and EIV,
are plotted as a function of the soil moisture content. It will be recalled that whilst the samples of experiment set EII were subjected to freezing, those of experiment set EIV were not. It can be seen that the values of both
pw and st for experiment set EIV are consistently
higher than the corresponding values for experiment set EII at all moisture contents within the range studied. Furthermore, the relative magnitude of the
difference increases with decreasing moisture
content. For experiment set EIV, the fall in tensile strength predicted by the theory appears to have occurred between the moisture contents of 0.2336 and 0.2325 g/g. Indeed, this moisture content range though slightly higher, corresponds closely with that observed for experiment set EII (i.e. 0.2261± 0.2240 g/g). On close examination of the equivalent pore diameter, the results show that the same size range of inter-aggregate pores were emptied in both
cases the range being 5.56±6.00mm for EII and
5.45±5.77mm for EIV.
These results show that freezing depresses the strength of inter-aggregate bonds. This means that further reductions in the energy required to crumble structured agricultural soils, can be achieved by per-forming crumbling operations on such soils as they dry from a frozen condition.
4.4. Effect of freezing on brittleness of soil
The diametric strain-to-failure, eD, determined
using Eq. (7), provides an index of the brittleness of the soil. Values of eD are plotted as a function of
moisture content for both experiment sets EII and EIV in Fig. 9. In spite of some degree of scatter in the results, it is evident from the ®gure that at any
moisture content, the values ofeD for EII are lower
than the corresponding values for EIV. The magnitude of the difference between the two appears to reduce as the soil further dries out. The immediate deduction
here is that freezing increases brittleness of the soil. Perhaps a more interesting implication of these results is that, due to increased brittleness, the integrity of soil aggregates as well as overall soil structure will be
Fig. 8. Bonding strength plotted against soil moisture content for experiment sets EII and EIV.pw, capillary bonding stress;st, soil tensile
strength.
better preserved if the soil is crumbled (say by a tillage operation) in the condition represented by EII than in that represented by EIV in Fig. 9.
5. Conclusions
The proposed capillary crumbling model accounts satisfactorily for the mechanics of crumbling in struc-tured agricultural soils where capillary bonding forces are predominant. The fall in inter-aggregate bonding strength (i.e. tensile strength) corresponding to the emptying of pores of a particular size class at a narrow soil suction range occurred as predicted by the model. This took place over a narrow range of soil moisture content. The greater the relative proportion of these pores within the soil, the more prominent will be the fall in the tensile strength of the soil.
When tillage and cultivation operations are carried out on relatively wet soils large plastic deformations occur and both the soil structure and integrity of aggregates are undermined. On the other hand, when these operations are carried out on rather dry, baked or cemented soils, much energy is expended and equip-ment and impleequip-ments are exposed to high risks of damage. The proposed capillary crumbling model can be exploited in the determination of friable and/or workable conditions in structured agricultural soils. Certainly, efforts to crumble the soil would be opti-mized by taking advantage of the fall in inter-aggre-gate bonding strength at a moisture content and soil suction where the risk of damage to the integrity of aggregates is relatively small. In temperate regions, this risk can be further minimized by performing crumbling operations on these soils as they dry from a frozen condition. This should lead to an optimal combination of the energy required to crumble the soil as well as the quality of tilth (soil structure) produced by the crumbling operation.
Acknowledgements
The ®rst author wishes to thank Wageningen Uni-versity for the award of a Postdoctoral Research Fellowship.
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