A method for prediction of soil penetration resistance

Transcription

1 Soil & Tillage Research 93 (2007) A method for prediction of soil penetration resistance A.R. Dexter *, E.A. Czyż, O.P. Gaţe Institute of Soil Science and Plant Cultivation (IUNG-PIB), ul. Czartoryskich 8, Pulawy, Poland Received 2 January 2006; received in revised form 24 April 2006; accepted 27 May 2006 Abstract A new equation for predicting penetration resistance of soil is presented. The equation contains two main additive terms: the first is a measure of the degree of compactness of the soil and the second gives the contribution of pore water to the soil strength. It is proposed that these terms are applicable to soils of different texture, at different bulk densities and at different water contents. The equation is calibrated and tested using values of penetrometer resistance measured in the field at a range of locations in Poland. Predictions from the equation are compared with predictions from two other published equations. It is shown that the performance of the proposed equation is superior to the other two, at least for the Polish data set used in this work. On the basis of the assumption that the proposed equation is correct, predictions of penetrometer resistance are made using pedotransfer functions to illustrate typical effects of soil texture, bulk density and water content. # 2006 Elsevier B.V. All rights reserved. Keywords: Effective stress; Pedotransfer functions; Penetrometer resistance; S-theory 1. Introduction Penetration resistance of soil is usually measured with a penetrometer. Penetrometer resistance is widely measured because it provides an easy and rapid method of assessing soil strength. The theory of penetrometers is presented in several publications (e.g. Bengough et al., 2001). In these publications it may be seen that the resistance to penetration is governed by several more basic properties including soil shear strength, soil compressibility and soil/metal friction. Unfortunately, each of these factors is difficult to measure or predict, and so approaches using these factors do not facilitate the use of penetrometers. The penetration resistance is itself of little value. However, it correlates with several other properties that are themselves of direct practical importance. For example, the draught force (and hence the energy requirements) of tillage implements (e.g. Dawidowski et al., 1988), vehicle trafficability (e.g. Dexter and Zoebisch, 2002) and the growth (or elongation rate) of plant roots (e.g. Taylor and Ratliff, 1969) in the soil. These practical aspects are extremely difficult and time consuming to measure and to study directly. Therefore, penetration resistance is often used as a surrogate measurement. There is a need to be able to predict penetrometer resistance from basic soil properties such as the soil composition, bulk density and water content. It is generally found that for any one soil, it is quite easy to produce an empirical equation that accounts for differences in bulk density and water content. However, the predictions are often not so good when different soils are being compared. A typical equation used for prediction of penetrometer resistance, Q, is that used by da Silva and Kay (1997): * Corresponding author. address: tdexter2@iung.pulawy.pl (A.R. Dexter). Q ¼ au b D c (1a) /$ see front matter # 2006 Elsevier B.V. All rights reserved. doi: /j.still

2 A.R. Dexter et al. / Soil & Tillage Research 93 (2007) which may also be written in terms of natural logarithms as ln Q ¼ ln a þ b ln q þ c ln D (1b) where, D is the bulk density of the soil, u is some measure of the soil water content and a, b and c are adjustable parameters. Eqs. (1) can work quite well for any one soil. When a range of soils is considered, then additional pedotransfer functions (PTFs) are often used with the form a ¼ A 1 þ A 2 ðclayþþa 3 ðomþþ b ¼ B 1 þ B 2 ðclayþþb 3 ðomþþ c ¼ C 1 þ C 2 ðclayþþc 3 ðomþþ (2) where, clay is the soil clay content, OM the organic matter content, and the coefficients A i, B i and C i are determined by experiment and regression. This approach typically uses at least nine different coefficients. However, it cannot really be expected that an equationsuchaseq.(2) based on D and u could be very successful. Common experience shows that bulk density is not a good measure of the degree of compactness of soil. For example, a bulk density of 1.4 Mg m 3 is a high value for a clay but is a low value for a sand. Similarly a water content of a clay that feels dry may be sufficient to make a sand feel wet. Therefore, bulk density and water content do not seem to form a very sound basis for a prediction equation. Canarache (1990a, 1990b) produced a method and a computer program called PENETR for predicting Q. This uses more complex relationships for the effects of water content, clay content, bulk density, etc. Another prediction equation has been proposed recently by To and Kay (2005). This takes the form Q ¼ ah b ch (3) Here, h is the pore water suction which is numerically equal to the modulus of C (the matric water potential) and the terms a, b and c (which do not have the same values as those given in Eqs. (1) and (2)) are determined as PTFs using equations of similar type to those shown in Eq. (2), in this case having a total of up to 13 coefficients. The values of h were adjusted in the laboratory. To and Kay (2005) obtained a value of r 2 = 0.47 when Eq. (3) was applied to undisturbed samples of Canadian soils of all textures. However, the value of r 2 could be increased if the equation was applied only to soils having a limited range of texture. Practical application of Eq. (3) requires either measurement of water potential (e.g. using tensiometers) or the prediction of water potential using measurements of soil water content in combination with a water-retention curve that has been measured on the same soil at the same density. It should be noted that Canarache (1990a, 1990b) and To and Kay (2005) did their measurements in the laboratory on soil samples collected from the field. With this approach, the values of penetration resistance, bulk density and water content were all measured on the same samples that were contained in steel cylinders. This approach is not possible with measurements of penetration resistance made in the field. Dexter (2004a, 2004b, 2004c) defined a quantity S as the slope, du/d (ln h), of the water retention curve at its inflection point. He noted that values of S appeared to have the same physical meaning in soils of all textures. For example, it was observed that growth of plant roots ceased at around S = 0.02, probably because of mechanical impedance as can be measured with a penetrometer. This led to the idea that S may be related to penetrometer resistance and this is the subject of this paper. In this paper, we propose and test the equation 1 Q ¼ a þ b þ cs 0 (4) S where S is from Dexter (2004a, 2004b, 2004c) and s 0 is the effective stress. S was identified as an index of soil physical quality and 1/S is a measure of the degree of compactness of soil. It should be noted that this is different from the measure of degree of compactness used by Håkansson (1990). However, the term degree of compactness is also used here because it conveys exactly the meaning of (1/S). The effective stress term, s 0, gives the contribution of the pore water to soil strength. This term has two components: a pore water pressure term and a term due to the surface tension in water menisci between the soil mineral particles (Towner and Childs, 1972). Vepraskas (1984) showed that the water menisci term could be ignored for degrees of saturation, x > 0.4. The resulting simplified equation was used successfully by Mullins and Panayiotopoulos (1984) and by Whalley et al. (2005), and will also be used here. Because the evidence suggests that values of S and s 0 have the same physical meanings in all soils, it seemed possible that Eq. (4) may be applicable to widely different soils with only its three coefficients a, b and c. It should be noted that the effects of clay and organic matter contents (and other factors) are already included

3 414 A.R. Dexter et al. / Soil & Tillage Research 93 (2007) in Eq. (4) through the two terms S and s 0. The purposes of this paper were to test Eq. (4) and to compare its performance with that of the Canarache (1990a, 1990b) and the To and Kay (2005) models. 2. Materials and methods 2.1. Soils The measurements were made and samples were collected from agricultural fields in different locations in Poland. The positions of the locations were measured by GPS for reference purposes and will enable the same positions to be studied again in future, if required. The samples represented soils with several genetic origins including: glacial till, loess and alluvium. Penetration resistance was measured and soil samples were collected at depths of 10, 20, 30, 40 and 50 cm as much as possible. In some cases, the soil was too dry and strong below the normal depth of tillage (around 25 cm) for penetrations and sample collection to be carried out. In these cases, only the plough layer was measured and sampled. A total of 85 different soil layers are represented. Samples of these soils were all measured, collected, stored and analysed by the same people and in the same way. They, therefore, comprise a rather reliable data set having consistent measurement errors. The particle size distributions of the soils were determined by sieving and sedimentation and the organic matter contents were measured by wet oxidation. The samples were not collected in the period immediately following tillage in the spring when the spatial variability of soil physical properties is high, but mostly in late June, July or early August which is just before or just after harvest. At the time of sample collection, the soil had settled to a quasi-equilibrium state. The crops in the fields were mostly barley or wheat. Although visible wheel tracks were avoided, it is possible that earlier wheel tracks, that were no longer visible, may have contributed to spatial heterogeneity. Sample collection for measurement of particle size distribution, bulk density, water content, and water retention characteristics were made from an area of approximately 1 m 2 in each field. Penetrometer penetrations were made in an area of about 2 m radius from the centre of the sample collection area. Therefore, all samples and all measurements were made as nearly as practically possible from a single point in each field. This was in an attempt to reduce the effects of spatial variability to a minimum Penetrometer resistance A model CP20 cone penetrometer (Agridry RIMIK Pty. Ltd., Toowoomba, Australia) was used in the field at all locations. This measures the mean vertical stress required for penetration of a steel cone of 12.8 mm diameter and 308 total included angle. The maximum value of stress that can be recorded is Q = 5000 kpa. The penetrometer records electronically the value of Q at intervals of 2.5 cm. The data were subsequently down-loaded to a computer for analysis. We used every fourth value to give the values of Q at 10, 20, 30, 40 and 50 cm depth. Ten replicate penetrations were done for each location. In some cases, penetration into the sub-soil was not possible because of the high soil strength. However, these missing data were not ignored but were taken into account. To do this, the value 9999 was written into the data file where data were missing. Then we did not use mean values of Q but median values. Therefore, if 1, 2, 3 or 4 of the 10 replicate data were missing then the median value was unaffected and was used to represent the soil strength. If five or more values were missing, then the remaining values were not used. For normally distributed values, the median and the mean are similar Soil bulk density and water content Bulk density was measured on soil samples collected in 100 cm 3 stainless steel cylinders of approximately 5 cm height. Each cylinder was then closed at both ends with metal caps and was then placed in a polythene bag that was closed tightly. This ensured that the samples would remain at their field water content. Usually, four replicate samples were taken from each layer although in a few cases there were more (e.g. 8). These were dried at 105 8C for 48 h in an oven. The dry mass of the soil divided by the cylinder volume gave the bulk density, D (g cm 3 =Mgm 3 ). The gravimetric water content, u (kg kg 1 ) was calculated as the mass of water in the soil sample divided by the mass of the dry soil Water retention characteristics Soil water retention was measured as follows. Samples were collected in 100 cm 3 stainless steel cylinders of approximately 5 cm height. Each cylinder was then closed at both ends with metal caps and was then placed in a polythene bag that was closed tightly. This ensured that the samples would remain at their field water content. The importance of preventing

4 A.R. Dexter et al. / Soil & Tillage Research 93 (2007) samples from drying has been shown by Baumgartl (2003). He showed that drying a soil to water contents drier than it has experienced before can cause irreversible shrinkage with corresponding changes to the pore size distribution and the water retention characteristic. Samples were not collected from every 10 cm depth layer, but usually only from three depth layers: the middle of the plough layer (e.g cm depth), the compaction pan (e.g. at 30 cm depth), and from the sub-soil (at 40 or 50 cm depth). All samples were from well-defined soil layers. The water retention characteristic for each layer was measured at 11 different pore water suctions: h = 10, 20, 40, 80, 250, 500, 1000, 2000, 4000, 8000 and 15,000 hpa. Sample height was approximately 5 cm for the first four suctions, 2.5 cm at 250 hpa and 1 cm for the higher suctions. The 2.5 cm samples were prepared by removing the top half of the soil from cylinders with a spoon. The 1 cm samples were prepared by crumbling the soil into small aggregates. These aggregates were still very large compared with the size-scale of the soil features being investigated at those suctions. The use of aggregates ensures that there are many points of contact between the soil and the ceramic pressure plates. Larger samples were used at the lower suctions in order to have samples that were large compared with the sizes of the structural features being investigated (i.e. representative samples ). Smaller samples (i.e. samples of lower height) were used at the higher suctions in order to reduce the time for equilibration of the soil water. Sample size is always a compromise between these two conflicting requirements. Two different replicates were measured at each suction, therefore, 22 samples were used to generate each water retention curve. It should be noted that suctions are used here because they are necessary in the van Genuchten (1980) equation (suction = matric water potential, where the matric water potential is negative in unsaturated soils). However, the van Genuchten equation works only with positive numbers. The sets of (u, h) data were fitted to the van Genuchten (1980) water retention equation: u ¼ðu sat u res Þ½1 þðahþ n Š m þ u res (5) where, u (kg kg 1 ) is the gravimetric water content at a suction h, u sat and u res, are the saturated and residual water contents, respectively, h (hpa) is the pore water suction, a (hpa 1 ) is a reciprocal suction that is characteristic for the soil, and m and n are dimensionless variables that describe the shape of the curve. However, m and n were not considered as independent variables but were assumed to be related by the Mualem (1976) constraint: m ¼ 1 1 (6) n The non-linear Eq. (5) was fitted iteratively to the experimental data for each soil using the Levenberg Marquardt method (Marquardt, 1963). Because not every depth layer was characterized, the van Genuchten parameters for 15 cm depth were used with the penetration resistance at both 10 and 20 cm depth. Similarly, the parameters for 40 or 50 cm depth were used to characterize both the 40 and 50 cm depths S and effective stress The value of S was calculated as described by Dexter (2004a) from the parameters of the fitted van Genuchten (1980) equation using S ¼ nðu sat u res Þ 1 þ 1 ð1þmþ (7) m The value of the effective stress was calculated from s 0 ¼ xh (8) where x is the degree of saturation (=(u u res )/ (u max u res )) and h (hpa) is the prevailing pore water suction calculated using the inverted form of Eq. (5): hðxþ ¼ 1 a ½x 1=m 1Š 1=n (9) 3. Results and discussion The soils used had clay contents in the range from 2 to 25% with an arithmetic mean of 9.9%. Organic matter (OM) contents ranged from 0.03 to 2.4% with a mean of 1.21%, and bulk density (D) values ranged from 1.24 to 1.81 g cm 3 with a mean of 1.54 g cm 3. The values of bulk density in any one soil had a mean standard deviation of g cm 3. The mean gravimetric water content of the soils was 0.15 kg kg 1. In a few locations, the penetrometer was able to penetrate to its full working depth with every replicate. Tests on these data using the Shapiro-Wilk normality test show that in the majority of cases, the values of penetrometer resistance, Q, at a given depth were normally distributed to a level of statistical significance of P = We took this as justification of the use of

5 416 A.R. Dexter et al. / Soil & Tillage Research 93 (2007) median values for locations where there were missing values. Although 15 out of the total of 85 soil layers had degrees of saturation less than 0.4, we decided to use Eq. (8) in every case because of its simplicity and ease of use. Measured values of penetration resistance, Q, were regressed against 1/S and s 0. This resulted in the equation Q ¼ 328 ð319þ þ 37:39 ð6:05þ r 2 ¼ 0:375; p < 0:001 1 þ 1:615 S ð0:399þ s0 kpa; (10) The three coefficients in Eq. (10) were different from zero at the p = 0.2, p < and p < levels of significance, respectively. In principle, the equation could have been fitted without the constant term because it is not significantly different from zero. However, it was decided to keep it in order to have residual values that were normally distributed. Interestingly, when an interaction term (s 0 /S), was included it was found to be not statistically significant (T = 0.17), and did not increase the value of r 2. The low value of r 2 requires some comment and explanation. It is at least in part due to the spatial variation of soil properties in the field. As discussed above, the penetration resistance, water content and bulk density, and the water retention characteristics were all made using different soil samples. The extent to which these all used representative soil is unknown. Similarly, the water retention characteristics were not determined for every soil layer as described at the end of Section 2.4. Table 1 provides some information about the variability of key physical properties of soils of different genetic origin used in the experiments. The Table 1 Representative values of the coefficients of variation (COVs) found for the measurements of bulk density, D, gravimetric water content, u, and penetrometer resistance, Q Genetic origin Plough layer Subsoil D u Q D u Q Alluvium Loess Glacial till Separate values are given for the plough layer and for the subsoil layers for soils of the three different genetic origins used in the experiments. The values are for a single depth at a single point and on a single measurement date. They do not include between-site variation. variabilities are expressed as mean values of the coefficient of variation (standard deviation divided by the mean). There were no statistically significant correlations between the values of D and u even though these were measured on the same samples. It can readily be shown that the variations in D and u do not fully account for the observed variations in Q. For example, if the value of D is set 1 standard deviation higher and the value of u is set 1 standard deviation lower than some measured value (both of which would tend to increase Q), then the predicted value of Q increases by only about 6%. We, therefore, conclude that factors other than D and u contribute to the values of Q measured in the field. The Pearson correlation coefficient between measured values of Q and those predicted using Eq. (10) is: R ¼ 0:612; p < 0:001 (11) This may be compared with that between measured values of Q and those predicted using the Canarache (1990a, 1990b) method for the same set of Polish soils: R ¼ 0:532; p < 0:001 (12) Although Eq. (11) shows a higher correlation coefficient for Eq. (10), this is partly to be expected because Eq. (10) was tested using the Polish soil data used in its development. However, the Canarache equations were developed using data for Romanian soils having on average higher clay contents. When we compared the measured values of Q with those predicted using Eq. (3) using To and Kay s coefficients for loam for all the soils, we obtained only R ¼ 0:274; p ¼ 0:21 (13) When their coefficients for sand were used, R was smaller. We attribute the small value of R in Eq. (13) to the fact that pore water suctions, h, were here estimated from measured water contents in combination with the inverted van Genuchten equation (Eq. (9)). This is in contrast with the work of To and Kay (2005) who were able to control the values of h in the laboratory. Another factor is that To and Kay s equations were developed using Canadian soils, but were tested here on Polish soils. The fit of Eq. (10), as measured by r 2,islow.We believe that this is largely due to the spatial variation of the soil physical properties in the field and because the water content, bulk density and water retention characteristics were measured on different soil samples. Additionally, values of pore water suction, h, must be estimated from measured soil water contents in

6 A.R. Dexter et al. / Soil & Tillage Research 93 (2007) Table 2 Typical values of S for the 12 FAO/USDA soil texture classes together with the parameters used in their calculation FAO/USDA texture class % Clay % Silt OM (%) D (Mg m 3 ) u sat (kg kg 1 ) a (hpa 1 ) n S cl sa cl si cl cl l si cl l sa cl l l si l si sa l sa sa Values of organic matter content (OM) and bulk density, r, were obtained as described in Dexter (2004a). The values of the parameters u sat, a and n of Eq. (5) were calculated using the values for clay, silt, OM and r in the pedotransfer functions of Wösten et al. (1999). Notes: sa = sand, si = silt, l = loam, cl = clay. combination with the inverted form of the van Genuchten equation (Eq. (9)) the parameters of which also have associated measurement errors and spatial variability. One of the main assumptions that has been made is that penetrometer resistance is directly proportional to effective stress. No account has been taken of the fact that soil shear strength increases with the product of the effective stress and the coefficient of internal friction, tan w, of the soil. Although a value of w of around 358 is typical for agricultural soils, the actual range varies from 0 to 458. The value of w tends to be larger with increasing particle size and with increasing particle angularity (Dexter and Tanner, 1972). It is also true that neither friction between the penetrometer cone and the soil nor possible cementation between soil particles is accounted for in the approach used here. The effects of soil/penetrometer friction could be removed by the use of a rotating penetrometer, as used by Whalley et al. (2005). Those authors found that effective stress alone could be used to predict penetrometer resistance in soils of low density, but not in soils of high density. This is exactly what is predicted by Eq. (10): at low densities, S is large and the effective stress term dominates; however, at high densities, S is small and effective stress alone is not sufficient for prediction of Q. equation in terms of soil composition and bulk density. These are the same data that were used for illustrative purposes in Dexter (2004a, 2004b, 2004c). This enables derived results to be compared directly. Fig. 1 shows the values of S that correspond to different values of penetrometer resistance, Q, at two values of water matric suction, h. Both values of h correspond to field capacity. However, h = 100 hpa is the value used in most countries for the suction to which saturated soil will drain, whereas, h = 330 hpa is the value used in the USA. The values were calculated by setting the value of h and then calculating the corresponding values of u for the different soil texture classes. Then the value of D was iterated until the value of Q was 1000, 1250, 1500, etc. (kpa). The values in the graph are the means for all the 12 FAO/USDA soil texture classes shown in Table Examples of some predictions For the purposes of these predictions we use the data for different soil textural classes presented in Table 2. We also use the PTFs of Wösten et al. (1999) which give the parameters of the van Genuchten water retention Fig. 1. Predicted values of the index of soil physical quality, S, that correspond with values of penetrometer resistance, Q, for two different values of soil water suction, h.

7 418 A.R. Dexter et al. / Soil & Tillage Research 93 (2007) Fig. 2. Values of bulk density, D, for different values of soil clay content that are predicted to give various values of penetration resistance, Q, at a soil water suction of h = 100 hpa. By iteration, it is also possible to estimate the values of soil bulk density for soils with different clay contents (as given in Table 2) that will give various values of penetrometer resistance, Q, when the soil is at field capacity (defined as h = 100 hpa). The results are shown in Fig. 2. These curves were fitted to the following equations: For Q = 1500 kpa when h = 100 hpa: clay D ¼ 1:107 þ 0:774 exp ; r 2 ¼ 0:989 22:47 (14) For Q = 2000 kpa when h = 100 hpa: clay D ¼ 1:203 þ 0:785 exp ; r 2 ¼ 0:989 32:75 (15) For Q = 2500 kpa when h = 100 hpa: clay D ¼ 1:282 þ 0:777 exp ; r 2 ¼ 0:991 39:38 (16) For Q = 3000 kpa when h = 100 hpa: clay D ¼ 1:348 þ 0:762 exp ; r 2 ¼ 0:991 43:61 (17) Predicted values of penetrometer resistance, Q, as a function of gravimetric water content, u, are shown for three soil texture classes in Fig. 3. This was calculated using the representative soil properties as given in Table 2. It should be noted that the effect of water content occurs entirely through the effective stress. Fig. 3. Predictions of how penetrometer resistance, Q, varies with gravimetric water content, u, for three soil texture classes. As explained above, the results presented in Figs. 1 3 are based on predictions using the pedotransfer functions of Wösten et al. (1999). They, therefore, represent predictions based on the average properties of European soils of the given texture classes. It must not be assumed that these predictions are accurate for any particular soil. However, it may be assumed that the trends and effects that they illustrate are typical. 5. Conclusions The equation (Eq. (10)) that has been proposed for penetrometer resistance is the sum of two simple terms: one represents the degree of compactness of the soil, whereas, the other represents the effect of water. The first term is the reciprocal of Dexter s (2004) index of soil physical quality. The second is the effective stress due to pore water pressure. We conjecture that this equation is applicable to all soil types and texture classes without any change in equation parameters. However, this needs to be tested in future research. The equation that is proposed (Eq. (10)) is both logical and physically meaningful. Future research should be aimed at testing this proposed equation in a wider range of soil types. The equation could perhaps be improved by taking account of friction. Acknowledgement Ms. O.P. Gaţe would like to thank the European Commission Proland project (contract number QLK4- CT ) for the support that enabled this work to be done.

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