Soil & Tillage Research 82 (2005) 29–37 www.elsevier.com/locate/still
SIDASS project Part 3. The optimum and the range of water content for tillage – further developments A.R. Dexter a,*, E.A. Czyz˙ a, M. Birka´s b, E. Diaz-Pereira c, E. Dumitru d, R. Enache d, H. Fleige e, R. Horn e, K. Rajkaj f, D. de la Rosa c, C. Simota d a
Institute of Soil Science and Plant Cultivation (IUNG), ul. Czartoryskich 8, 24-100 Pulawy, Poland b Szent Istvan University, Pa´terKa´roly u.1, 2130 Go¨do¨llo˝, Hungary c Institute of Natural Resources and Agrobiology of Seville, CSIC, Avda. Reina Mercedes 10, 41012 Seville, Spain d Research Institute for Soil Science and Agrochemistry, Bd. Marasti 61, 71331 Bucarest, Romania e Christian-Albrechts-University, Olshausenstrasse 40, D-24118 Kiel, Germany f Research Institute of Soil Science and Agrochemistry, Herman Otto u´t. 15, H-1022 Budapest, Hungary
Abstract The SIDASS project ‘‘A spatially distributed simulation model predicting the dynamics of agro-physical soil state within Eastern and Western Europe countries for the selection of management practices to prevent soil erosion based on sustainable soil–water interactions’’ required a method for estimating the dates (or soil water conditions) under which soil tillage operations could be performed. For this purpose, methods were developed for estimating the optimum and the range of soil water contents for tillage. These methods are based on the soil water retention curve. In this paper, we further develop the method in two ways. First, we take account of the fact that the soil properties: clay content, organic matter content and bulk density are not independent. This is done through the use of simple pedo-transfer functions which are based on measurements on many soils. Second, we present a simplified and more rapid method for estimating the lower (dry) limit for tillage. This enables this lower limit to be calculated using a computer spreadsheet instead of through tedious iterative calculations which were previously obtained with a special computer program. Examples are given for the tillage limits which take account of the interdependencies between the contents of clay, the content of organic matter and the bulk density. Estimated typical values of the tillage limits are presented for all the soil texture classes in the FAO/USDA classification system. Additionally, it is shown that the range of water contents for tillage is expected to decrease with decreasing soil physical quality as measured by S. # 2005 Elsevier B.V. All rights reserved. Keywords: Pedo-transfer functions; Soil physical quality; Water retention curve; Van Genuchten equation
1. Introduction * Corresponding author. Tel.: +48 81 886 3421; fax: +48 81 886 4547. E-mail address:
[email protected] (A.R. Dexter).
Part of the SIDASS project required estimation of conditions under which tillage operations could be
0167-1987/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.still.2005.01.005
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performed without damage to the soil structure as would occur if the soil is too wet, and without excessive use of energy as would occur if the soil is too dry. Accordingly, a simple theory was developed and published which enabled the optimum and the range of water contents for tillage to be determined in terms of the water retention curve of the soil (Dexter and Bird, 2001). This is especially useful because the parameters of the van Genuchten equation for water retention are available as pedo-transfer functions. In the original work, factors in the pedo-transfer functions (e.g. clay and organic matter contents and soil bulk density) were considered to be independent variables, and their effects on the optimum water content for tillage and the tillage limits were investigated and reported separately. However, it was evident that bulk density was the factor most affecting the predicted soil water contents for tillage. It seemed likely that the effects of other factors such as clay content and organic matter content were mainly indirect through their effects on the bulk density. In this paper, we now develop and incorporate a simple pedo-transfer function for the soil bulk density so that we can look more realistically at the typical effects of soil composition on the optimum water content for tillage and on the trends in the tillage limits that might be expected to occur in the field. Whereas the pedo-transfer functions enabled the effects of different factors to be separated, some of the factors are now recombined in a special way to take account of their interdependence in the field. We also develop and propose a simplified method for estimating the lower (dry) tillage limit that enables this to be calculated more easily. Additionally, we illustrate the effect of soil physical quality, as described by Dexter (2004a,b,c), on the range of water contents for soil tillage.
Here, uSAT and uRES are the water content at saturation and the residual water content, respectively, a is a scaling factor for the water potential, and m and n are parameters which govern the shape of the curve. In this paper, all water contents are gravimetric. Eq. (1) fits many soils well, although there are some exceptions that include soils which have a bi-modal pore structure. In this paper, we assume that soil water retention is described by Eq. (1). It is useful to note that Eq. (1), when plotted as ln(h) against u, has only one characteristic point. This is the inflection point where the curve has zero curvature. The curve at its inflection point has two characteristics: its position and its slope. As shown by Dexter and Bird (2001), the optimum water content for tillage, uOPT, may be identified with the water content at the inflection point of the water retention curve, that is its position. In terms of the van Genuchten equation, this is given in general by 1 m uINFL ¼ ðuSAT uRES Þ 1 þ þ uRES (2) m The modulus of the optimum water matric potential for tillage (i.e. the potential at the inflection point) is given by 1 1 1=n hINFL ¼ (3) a m Eqs. (2) and (3) give estimates of the status of the soil water at the optimum conditions for tillage. Dexter and Bird (2001) suggested that the upper (wet) limit for tillage could be estimated as fixed proportion (they chose 0.4) of the distance between the optimum water content and the water content at saturation. In terms of the parameters of the water retention curve using the equation uUTL ¼ uINFL þ 0:4ðuSAT uINFL Þ
2. Theory The theory was given in full by Dexter and Bird (2001), and will only be summarized here. It is based on the van Genuchten (1980) equation for soil water content, u, as a function of applied water potential (or ‘‘suction’’), h: u ¼ ðuSAT uRES Þ½1 þ ðahÞn m þ uRES
(1)
(4)
The lower (dry) limit for tillage was defined arbitrarily by Dexter and Bird (2001) as the water content at which the soil strength was twice its value at the optimum water content for tillage. They estimated this from a simplified form of effective stress theory as used by Greacen (1960) and Mullins and Panayiotopoulos (1984). The dominant role of water in controlling the strength of agricultural soils has been shown using effective stress theory by Giarola et al.
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(2003) and Vepraskas (1984). To a first approximation, we may write that tOPT ¼ kxOPT hOPT
(5)
and tLTL ¼ kxLTL hLTL ¼ 2tOPT
(6)
where the x-values are the degrees of saturation = u/ uSAT. The coefficient, k, is assumed to be a constant the value of which depends on the type of strength measurement. In this paper, the interest is only in relative strength values, and so the value of k need not be considered. The value of hLTL, of course, has a corresponding value of water content, uLTL, at the lower tillage limit. More generally, account also needs to be taken of the contribution to soil strength due to surface tension forces in the soil water menisci between soil particles in unsaturated soil (e.g. Towner and Childs, 1972). This effect starts to become significant when soil dries below about x = 0.4 and becomes dominant when soil is drier than about x = 0.3 (Vepraskas, 1984). Therefore, this refinement is probably not necessary for the situations considered here where the soils are usually only slightly drier than optimum. Additionally, we shall consider the slope, S = du/ d(ln h), of the retention curve at the inflection point. If we use Eq. (1), then we obtain the analytical solution 1 ð1þmÞ S ¼ nðuSAT uRES Þ 1 þ (7) m
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replicates of 20 kg) to determine the amount of clods >50 mm. Measurements of the bulk density of 93 soil horizons of Polish agricultural soils were made by sampling in 100 mL stainless steel cylinders. Additionally, the particle size distributions were determined by sieving and sedimentation using standard methods. The organic matter content was measured by wet oxidation. The correlation between organic matter and clay content was investigated using results from samples from the tilled layers of 210 Polish soils. As in the earlier paper (Dexter and Bird, 2001), the van Genuchten equation for the water retention characteristic was fitted using the Mualem (1976) restriction: 1 (8) m¼1 n 4. Results and discussion 4.1. Tillage results The amount of clods larger than 50 mm produced, expressed as a percentage of the total tilled soil, is shown as a function of gravimetric water content at the time of tillage in Fig. 1 (left). It can be seen that there is a distinct minimum in the amount of clods produced at a
where S has been shown to be a useful measure of soil physical quality (Dexter, 2004a,b,c) that is positively correlated with soil friability (Dexter, 2004b), and negatively correlated with the amount of clods produced when tillage is done at the optimum water content (Dexter and Birka´ s, 2004).
3. Methods Tillage experiments were done in Hungary using a mouldboard plough on a soil with contents of clay and silt of 40 and 28 kg (100 kg)1, respectively. Soil water content varied naturally in the field and was measured twice every day. Tillage was done over a range of water contents in approximate steps of 2 kg (100 kg)1. The resulting tilled soil was sieved (6–10
Fig. 1. Clod production during tillage as a function of the gravimetric water content at the time of tillage. The left-hand graph shows the measured points and the optimum water content for tillage, uOPT. The right-hand graph shows the fitted quadratic equation with the upper and lower tillage limits, uUTL and uLTL, and the range of water contents for tillage, R.
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water content of about 21.5 kg (100 kg)1. The water content at this minimum is defined as the optimum water content for tillage, uOPT. This optimum is well illustrated by the data shown in Fig. 1 (left). Fig. 1 (right) shows the fitted quadratic equation. This is used for clarity to show the estimated upper and lower tillage limits, and also the range of water contents for tillage, R. It is interesting to note that, for this soil, the range of water contents for tillage is not limited by the amounts of clods produced, but by soil strength (at the lower tillage limit) and by potential soil damage by plastic deformation (at the upper tillage limit). The amounts of clods produced are governed by a different factor as discussed by Dexter and Birka´ s (2004). 4.2. Effects of soil composition on bulk density The values of bulk density, D, for the Polish soils were regressed against the values of clay content, C, and organic matter content, OM. The equation used was 1 ¼ a þ bC þ cOM (9) D We feel that it is more logical to use the reciprocal of the bulk density (i.e. the specific volume or volume per unit mass of solids) because it is better to have the mass (which is constant) in the denominator. Unit mass of soil is also in the denominators of the C and OM terms, and this therefore gives a common basis for all the terms in Eq. (9). The resulting equation is 1 ¼ 0:598ð0:020Þ þ 0:0203ð0:0049ÞOM; D
(10)
In this case, there is a significant effect of clay content, C (% or kg (100 kg)1), but this is much smaller than that of organic matter content, OM. We do not know the precise reason for the apparent differences in the results between Polish and the Dutch soils which are given by Eqs. (10) and (11). Simply for the purposes of illustration of the possible effects of soil composition, we use the mean of the above two Eqs. (10) and (11) in the next section: 1 ¼ 0:590 þ 0:00163C þ 0:0253OM (12) D It must be stressed that for prediction of the properties of particular soils in a region, regression equations (pedo-transfer functions) should be used that are appropriate for that particular region. Additionally, there is the result from analysis of 210 Polish soils from the tilled layer, that organic matter content is dependent on soil clay content. The results of regression show that OM ¼ 1:59ð0:07Þ þ 0:048ð0:007ÞC; r 2 ¼ 0:19; p < 0:001
(13)
Although this equation does not account for much of the variance, it does at least demonstrate a statistically significant trend. Eq. (13) is similar in form, but with significantly different coefficients, to those for UK soils with different management (Eqs. (6) and (7) in Dexter, 2004a). This again illustrates that, for prediction purposes, it is important to use equations which are appropriate for the soils being considered. However, to illustrate trends, Eq. (13) is used in this paper where necessary.
2
r ¼ 0:16; p < 0:001 Here D is in Mg m3 and OM is in % or kg (100 kg)1. Eq. (10) shows the strong effect of OM on soil-specific volume (or bulk density). There was no significant effect of clay content in these soils of low clay content (mean clay content = 7.5%). This result can be compared with a similar equation obtained for 91 Dutch clay soils (clay content > 8%) by Dr. J.H.M. Wo¨ sten (Alterra, Wageningen, personal communication): 1 ¼ 0:581 þ 0:00325C þ 0:0303OM; D r 2 ¼ 0:78
(11)
4.3. Effects of soil composition on water content for tillage The parameters of the van Genuchten equation for water retention were estimated using the pedo-transfer functions of Wo¨ sten et al. (1999). However, in every place in these pedo-transfer functions where the bulk density, D, appeared, we have used a value of D estimated from Eq. (12). In this way, we obtained estimates of the effects of soil clay content and organic matter content on the optimum water content for tillage and on the upper and lower tillage limits which take into account typical effects of these factors on the soil bulk density.
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Fig. 2. Estimated values for the optimum water content for tillage and the upper and lower tillage limits as functions of soil clay content at a constant organic matter content. The other assumptions are described in the text.
In Fig. 2 we show the predicted effects of clay content on the tillage limits. These values were calculated assuming a constant silt content of 35% and a constant organic matter content of 1.95%. The bulk densities were estimated using Eq. (12). The figure shows how the optimum water content for tillage and both the tillage limits are predicted to increase with increasing clay content of the soil. In Fig. 3, we show the predicted effects of organic matter content on the tillage limits. These values were calculated assuming a constant clay content of 15% and a constant silt content of 35%. The bulk densities
Fig. 3. Estimated values for the optimum water content for tillage and the upper and lower tillage limits as functions of soil organic matter content at a constant clay content. The other assumptions are described in the text.
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Fig. 4. Estimated values for the optimum water content for tillage and the upper and lower tillage limits as functions of soil clay content. Here, organic matter content is assumed to be positively correlated with clay content. Values are shown for the lower tillage limit for two different strength criteria. The other assumptions are described in the text.
were estimated using Eq. (12). The figure shows how the optimum water content for tillage and both the tillage limits are predicted to increase with increasing content of organic matter in the soil. In Fig. 4, we show predictions of the combined effects of soil clay and organic matter contents on the tillage limits. These were calculated using Eq. (13), and then the values of bulk density were calculated using Eq. (12). The resulting values were then used in the pedo-transfer functions of Wo¨ sten et al. (1999). Silt content was assumed to be constant at 35%. Values for the lower (dry) tillage limit are shown for two different criteria (the strength being twice its value at the optimum water content and being three times its value at the optimum water content). It can be seen that changing the criterion for the strength at the lower tillage limit has only a small effect on the predicted values of the water content at this limit. This is because the soil strength increases rapidly with decreasing water content. In Table 1, we present values of some important quantities for the different soil texture classes as used in the FAO and USDA classification systems. The values for clay and silt content were read from the centre of the area for each texture class on the standard FAO/USDA texture triangle. The extreme edges and corners of the texture triangle have not been considered, as these represent rather rare soils. The values of organic matter content were estimated using
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Table 1 Mean values for the particle size distribution (expressed in terms of the contents of clay and silt) for the 12 USDA/FAO soil texture classes FAO/USDA texture class
Clay (%)
Silt (%)
OM (%)
D (Mg m3)
usat (kg kg1)
a (h Pa)1
n
cl sa cl si cl cl l si cl l sa cl l l si l si sa l l sa sa
60 42 47 34 34 27 17 14 5 10 4 3
20 7 47 34 56 13 41 66 87 28 13 3
4.47 3.61 3.85 3.22 3.22 2.89 2.41 2.26 1.83 2.07 1.78 1.73
1.249 1.334 1.309 1.376 1.376 1.414 1.474 1.492 1.552 1.518 1.559 1.566
0.395 0.335 0.362 0.324 0.325 0.299 0.278 0.269 0.243 0.258 0.239 0.226
0.0217 0.0616 0.0220 0.0400 0.0226 0.0727 0.0314 0.0134 0.0045 0.0400 0.0534 0.0671
1.103 1.139 1.104 1.127 1.129 1.169 1.208 1.245 1.392 1.278 1.406 1.581
Notes: sa = sand, si = silt, l = loam, cl = clay. Values of organic matter content (OM) were estimated using Eq. (13) and then values of bulk density (D) were estimated using Eq. (12). The values of the parameters usat, a and n of Eq. (1) were calculated using the values for clay, silt, OM and D in the pedo-transfer functions of Wo¨ sten et al. (1999).
Eq. (13), and then the values of bulk density were calculated using Eq. (12). The resulting values were then used in the pedo-transfer functions of Wo¨ sten et al. (1999). Table 2 shows the optimum and the upper and lower tillage limits for the different FAO/USDA soil texture classes in terms of the values of the water content, u, as calculated using Eqs. (2)–(6) with the values given in Table 1. These values were calculated on the assumption that the residual water content, uRES, is zero and using the Mualem restriction in Eq. (8). Comment must be made about the small values of water potential (not shown) which are predicted for the upper (wet) tillage limit especially for sand and sandy
loam. In the field, water potentials smaller than h = 100 h Pa would usually not be found during tillage because such wet, coarse-textured soils would drain rapidly under gravity to the ‘‘field capacity’’ which corresponds to approximately h = 100 h Pa. A prediction from results which is not shown is that all four of the silty soils will present difficulties in tillage because even after they have drained to ‘‘field capacity’’, they will still be too wet (u > uUTL) and will be outside the range of water contents for tillage (uLTL < u < uUTL). This situation was described by Boekel (1959, 1965). Such soils can usually be dried sufficiently only by transpiration of plants because the process of evaporation from the soil surface is too slow.
Table 2 Values for the optimum water content for tillage and the upper and lower tillage limits calculated for the 12 USDA/FAO soil texture classes as quantified in Table 1 FAO/USDA texture class
uLTL (kg kg1)a
uLTL (kg kg1)b
uOPT (kg kg1)
uUTL (kg kg1)
cl sa cl si cl cl l si cl l sa cl l l si l si sa l l sa sa
0.292 0.231 0.267 0.229 0.228 0.195 0.170 0.155 0.111 0.141 0.106 0.068
0.291 0.230 0.266 0.228 0.227 0.194 0.169 0.154 0.111 0.140 0.106 0.077
0.314 0.256 0.287 0.251 0.250 0.221 0.199 0.188 0.159 0.177 0.155 0.140
0.347 0.287 0.317 0.280 0.286 0.252 0.231 0.220 0.192 0.209 0.188 0.174
a b
Values were calculated using the exact iterative procedure based on Eqs. (5) and (6). Values were calculated using the new method with Eq. (18).
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It can also be seen that the mean value of the ratio uOPT/uUTL is close to 0.9, which corresponds with field observations as discussed by Dexter and Bird (2001). 4.4. Improved method for estimation of the lower (dry) tillage limit In the original paper (Dexter and Bird, 2001), the lower tillage limit was defined as the water content at which the soil strength has twice the value that it has at the optimum water content for tillage. This was estimated through the use of an iterative procedure involving Eqs. (5) and (6). The rationale for this was that a farmer will normally use a tillage implement of such a width that his tractor will pull it efficiently when the soil conditions are optimum. If the soil strength is double, then his tractor will not pull the implement easily, and this effectively sets the dry limit for tillage of that soil-implement combination. The reader should remember, however, that there is no real lower tillage limit because soil can be tilled even when very dry without damage to its structure. The only consideration is how much time and energy a farmer is prepared to use for tillage. The lower tillage limit as defined above is, therefore, only an arbitrary, working definition based on practical soil management considerations. We now propose a method for estimating the lower tillage limit as defined above that does not require iterative calculations. It is based on the observation that the when soil is drier than a water potential of 1/a, then the shape of the water retention curve depends primarily on the parameter n. In order to investigate this, we used the values of the van Genuchten parameters given in Table 1 and also some for soils having larger values of n (in the range 1.8 < n < 2.5) which we have measured on some natural soils in Poland. It should be noted, however, that the majority of Polish soils fall in the range of 1.2 < n < 1.6. Values of log hOPT were calculated using Eq. (3) whereas values of log hLTL were calculated by the iterative procedure described previously. The differences, D(log h), were obtained from Dðlog hÞ ¼ log hLTL log hOPT
(14)
It should be noted that all logarithms here are to the base 10. The resulting values of D(log h) were regressed against the corresponding values of log n using the program MinitabTM. However, we can also
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take advantage of the fact that as n ! 1, then the soil remains saturated and from the theory of effective stress, the strength will increase proportionally with the suction, h. Therefore, the intercept of the regressions will be equal to the logarithm of the strength ratio required. The resulting regressions are presented in Eqs. (15) and (16) below. For strength to be twice as large: Dðlog hÞ ¼ log 2 þ 1:10 log n;
p < 0:001
(15)
ð0:05Þ
It is possible to produce similar equations for other strength ratios. For example, for strength to be three times as large: Dðlog hÞ ¼ log 3 þ 1:32 log n;
p < 0:001
(16)
ð0:09Þ
The above equations were developed using values of n in the range 1.09 < n < 2.5, and are sufficiently accurate for practical purposes over this range. It should be noted that this range of values of n covers all the FAO/ USDA soil texture classes discussed in the previous section, representative values for which are given in Table 1. The procedure for estimating the lower tillage limit is therefore as follows: (i) calculate the optimum water potential for tillage using Eq. (2), (ii) take the logarithm of this (to base 10), (iii) calculate D(log h) using Eq. (15), (iv) add (iii) to (ii) to get log(hLTL), (v) take the antilogarithm of (iv) to get hLTL. These calculation steps can be done easily on a simple spreadsheet without the need for any iterative procedures or special programs. Alternatively, it is possible to arrive at step (iv) directly using: 1 1 1=n log hLTL log þ log 2 þ 1:1 log n (17) a m or at step (v) directly using 2 1 1=n 1:1 n hLTL
a m
(18)
The water content at the lower tillage limit, uLTL, can then be estimated using the value of hLTL from Eq. (18) in Eq. (1).
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Fig. 5. Estimated value for the range, R, of water contents for tillage as a function of soil physical quality, S, for five Hungarian soils.
Eqs. (17) or (18) can be calculated on a computer spreadsheet, and provide an easier method for estimating the position of the lower (dry) tillage limit than the cumbersome iterative procedure described previously. Some comparisons of values of the water content at the lower (dry) tillage limit calculated by the two methods are presented in Table 2. 4.5. The range of water contents for tillage and soil physical quality, S The range, R, of water contents for tillage was calculated using R ¼ ðuUTL uLTL Þ
(19)
where uUTL and uLTL were calculated as described above. Additionally, S was calculated using Eq. (7). A graph of R against S for five different Hungarian soils is presented in Fig. 5. This shows clearly how the range of water contents for tillage deceases as soil physical quality, S, decreases. It should be remembered, however, that both R and S were calculated from the same water retention curves and are therefore not independent. Nevertheless, the correlation between the two calculated quantities is of interest.
5. Conclusions For soils for which the water retention characteristics have been measured, the optimum water content for tillage and the upper (wet) and lower (dry) limits
may be estimated directly using Eqs. (2), (4) and (18). For soils for which water retention data are not available, the water retention characteristics may first be estimated from basic soil data using pedo-transfer functions. Of course, measured values will always be more accurate than estimated values. The pedo-transfer functions of, for example, Wo¨ sten et al. (1999) enable the effects of different factors such as clay content, organic matter content and bulk density to be invstigated separately. However, in most cases, these factors are not independent but are strongly correlated. An example is the inverse correlation between organic matter content and bulk density. The exception is bulk density, the effects of which can considered alone because soil can be compacted without any change in composition. For the other factors, we have produced regression equations (Eqs. (9)–(13)) which recombine them in realistic ways. This enables the effects of the factors, in combinations which may be expected to occur in the field, on the tillage limits to be estimated. The new method which has been presented in Eq. (18) enables the lower (dry) tillage limit of soils to be estimated much more easily than by the previous iterative method which involved the use of a special computer program. This new method enables the values to be obtained easily on a standard computer spreadsheet. A comparison of the results obtained by the two methods as given in Table 2 shows that the results from Eq. (18) are very close to those obtained by the exact method of calculation. Pedo-transfer functions are very useful for showing trends in soil behaviour, however they must be treated with great caution when used for prediction purposes for particular soils. For example, the use of the clay content alone has severe limitations and different clay minerals such as montmorillonite, illite and kaolin would give different responses. Similarly, the suite of exchangeable cations associated with the clay influences the soil–water interactions. Nevertheless, the results which are presented above can be considered to show trends of behaviour which may be expected to be representative of typical European agricultural soils. The prediction that the range of water contents over which tillage may be done decreases with decreasing soil physical quality (i.e. with physical degradation) is consistent with the observations of Hoogmoed (1985) and with the observations of Australian farmers as
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heard by the first author. The implication is that management practices which increase the value of the soil physical quality, S, will also increase the range of water contents for tillage. Further observations in the field are needed to test these predictions. Acknowledgements The authors would like to thank the European Commission for their support of the SIDASS project under grant number ERBIC15-CT98-0106. They would also like to thank Dr. J.H.M. Wo¨ sten of Alterra, Wageningen, for providing Eq. (11) and for useful discussions. References Boekel, P., 1959. Evaluation of the structure of clay soil by means of soil consistency. Meded. Landbouwhogesch. Opzoekingsstn. Staat Gent XXIV, 363–367. Boekel, P., 1965. Handhaving van een goede bodemstructuur op klei en zavel gronden. Landbouwk. Tijdschr. 77, 842–849. Dexter, A.R., 2004a. Soil physical quality: Part I. Theory, effects of soil texture, density, and organic matter, and effects on root growth. Geoderma 120, 201–214. Dexter, A.R., 2004b. Soil physical quality: Part II. Friability, tillage, tilth and hard-setting. Geoderma 120, 215–226.
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Dexter, A.R., 2004c. Soil physical quality: Part III. Unsaturated hydraulic conductivity and general conclusions about S-theory. Geoderma 120, 227–239. Dexter, A.R., Bird, N.R.A., 2001. Methods for predicting the optimum and the range of soil water contents for tillage based on the water retention curve. Soil Tillage Res. 57, 203–212. Dexter, A.R., Birka´ s, M., 2004. Prediction of the soil structures produced by tillage. Soil Tillage Res. 79, 233–238. Giarola, N.F.B., da Silva, A.P., Imhoff, S., Dexter, A.R., 2003. Contribution of natural compaction on hardsetting behavior. Geoderma 113, 95–108. Greacen, E.L., 1960. Water content and soil strength. J. Soil Sci. 11, 313–333. Hoogmoed, W.B., 1985. Soil tillage at the tropical agricultural day. Soil Tillage Res. 5, 315–316. Mualem, Y., 1976. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 12, 513–522. Mullins, C.E., Panayiotopoulos, K.P., 1984. The strength of unsaturated mixtures of sand and kaolin and the concept of effective stress. J. Soil Sci. 35, 459–468. Towner, G.D., Childs, E.C., 1972. The mechanical strength of unsaturated porous granular materials. J. Soil Sci. 23, 481–498. van Genuchten, M.Th., 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44, 892–898. Vepraskas, M.J., 1984. Cone index of loamy sands as influenced by pore size distribution and effective stress. Soil Sci. Soc. Am. J. 48, 1220–1225. Wo¨ sten, J.H.M., Lilly, A., Nemes, A., Le Bas, C., 1999. Development and use of a database of hydraulic properties of European soils. Geoderma 90, 169–185.
