estimating soil water content from soil strength

~ Soil & age. K e s e a r c n

ELSEV I ER Soil & Tillage Research 31 (1994) 199-209

Estimating soil water content from soil strength 1

L.N . M i e l k e *'a, W.L . P o w e r s b, S. B a d r i b, A.J. J o n e s b

aSoil and Water Conservation Research Unit, US Department of Agriculture, Agricultural Research Service, 119 Keim Hall, East Campus, University of Nebraska, Lincoln NE, 68583-0915, USA

b Department of Agronomy, University of Nebraska, Lincoln, NE, 68583-0915, USA

(Accepted 12 January 1994)

Abstract

Variable rate application technology requires real time estimates of field water contents. This study was conducted to evaluate soil strength as a possible indicator of soil water content. The study involved measurement of soil strength with flat tip and cone penetro- meters on laboratory packed soil cores. Packing treatment varied from Proctor Test (PT) bulk densities to densities similar to those of cultivated field soils. Soils used in the study included 18 benchmark soil series representing eight soil orders. Soil samples were from the surface 300 mm depth and from a subsurface layer. Soil strength tests were run at PT densities for all 18 soils and at cultivated field densities for four of the 18 soils. Two equations were fitted to plots ofgravimetric water content versus soil strength using least squares nonlinear regression techniques. Predicted and measured water contents were in better agreement at the PT densities than at cultivated field densities. Sand content accounted for 36% of the variation in equation parameters at PT densities.

Keywords: Benchmark soils; Bulk density; Proctor density; Variable rate application technology; Water- strength relationships

1. Introduction

In agriculture, soil strength has been used to evaluate the effect o f tillage operations on soil physical properties, soil compact ion f rom wheel traffic and tillage tool shear plane, and restricted root deve lopment and thus reduced nutr ient and water uptake (Bradford, 1980; Bauder et al., 1981; Radcliffe et al., 1988; Hill, 1990; Lowry and Schuler, 1991 ). Recent advances in real t ime measurements

~Published as Journal Series No. 10130, Agricultural Research Division. *Corresponding author.

0167-1987/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI0167-1987(94)00382-0

200 L.N. Mielke et al. / Soil & Tillage Research 31 (1994.) 199-209

and position location have initiated research on applying herbicides and fertil- izers at variable rates to account for soil variations (Robert et al., 1992). This variable rate application technology (VRAT) requires the use of extensive pre- operation surveys or near instant (real t ime) determination of controlling parameters such as available nutrient contents of soils, weed populations, and soil water content. If real time determinations of soil water content can be made during field operations, then VRAT can provide an excellent opportunity for precise depth of planting and tillage under variable field conditions.

Soil strength has been related to water content using a variety of functions. Towner ( 1961 ) and Camp and Gill ( 1969 ) developed linear equations relating load failure (soil strength) to soil water suction as well as soil water content and cohesion forces. Mirreh and Ketcheson (1972) used multiple regression techniques to predict penetrometer resistance from soil water matric potential and bulk density. Williams and Shaykewich (1970) developed an exponential equation relating soil strength to soil water matric potential. Gerard ( 1965 ) expressed soil strength as an exponential function of water content. Both Nichols ( 1932 ) and Gerard ( 1965 ) found that soil strength increased with decreasing soil water to a maximum and then soil strength decreased sharply at lower water content. The objective of this research was to develop and test two equations for predict- ing gravimetric soil water content from soil strength. A secondary objective was to suggest possible use of the relationships and defining equations.

2. Methods and materials

Soil samples from 18 benchmark soils were used for Proctor Test (PT) density measurements. The 16 soils from the continental United States and the two from Hawaii represented eight soil orders. Samples were obtained from two depths: surface (0-300 mm) and the subsurface (300-600 mm). Surface samples were tilled or untilled depending on land use. The subsurface sample included soil be- low the tillage zone and for most soils was part of the B horizon. Physical and chemical characteristic data, series, and location of each soil are given in Table 1. Clay content ranged from 4 to 60%.

2.1. Proctor Test densi t ies

Soil samples were passed through a 2 mm sieve at field water content. PT density procedures (American Society for the Testing of Materials, 1985 ) were used over a range of gravimetric water contents including at least one water content greater than that associated with maximum bulk density. Gravimetric water content was used rather than volumetric water content to minimize the scatter of data caused by differences in bulk density. At each water content a soil strength determination was made on the molded soil sample using a flat tip (0.32, 0.645, or 2.15 cm 2 cross-sectional area, depending on soil strength) penetrometer.

L.N. Mielke et al. ~Soil & Tillage Research 31 (1994) 199-209 201

Table 1 Soil classification, location, texture and organic carbon (OC) content

Soil Great or Soil series Texture b Location Mineralogy Soil Clay Silt OC order ~ subgroup layer (%) (%) (%)

A Typic Crider SiL Kentucky Mixed Paleudalf SiCL

A Typic Miami L Indiana Mixed Hapludalf CL

E Typic Valentine S Nebraska Mixed Ustipsamment S

E Typic Yolo L California Mixed Xerothent L

I Ustoxic Kole Kole SL Hawaii Oxidic Humitropept

I Dystril Caribou L Maine Mixed Eutrochrept L

M Typic Walla Walla SiL Oregon Mixed Haploxeroll SiL

M Udic Barnes SCL North Mixed Haploborall SCL Dakota

M Typic Clarion L Iowa Mixed Hapludoll L

M Torrertic Pullman SiCL Texas Mont. Paleustoll SiC

M Typic Sharpsburg SiCL Nebraska Mont. Argiudall SiCL

O Tropeptic Wahiawa C Hawaii Kaol. Eutrustox

R Typic Mohave SCL Arizona Mixed Haplargid SL

R Ustollic Fort Collins SCL Colorado Mixed Haplargid SCL

U Typic Frederick SiL Virginia Mixed Paleudult SiCL

U Typic Cecil SL North Kaol. Haludult C Carolina

U Typic Rains SiL South Silic. Paleaquult SiL Carolina

V Udic Houston Black C Texas Mont. Pellustert C

1 25 73 2.14 2 34 64 0.33 1 22 50 1.23 2 34 34 0.58 1 06 05 0.81 2 04 02 0.41 1 26 54 1.31 2 26 54 0.86 1 14 38 3.46

14 46 2.37 14 42 1.52 18 67 1.09 15 69 0.53 26 36 2.17 28 36 0.96 21 28 1.31 22 30 0.83 34 51 0.92 43 44 0.7l 36 62 1.69 38 60 1.03 60 33 1.30

26 24 0,67 19 17 0,25 29 17 0.77 30 17 0.53 19 62 2.19 37 51 0.25 10 20 3.20 51 17 0.28 17 50 3.40 27 56 0.82 48 40 1.61 58 36 1.04

aA, Alfisol; E, Entisol; I, Inceptisol; M, Mollisol; O, Oxisol; R, Aridisol; U, Ultisol; V, Vertisol. bC, clay; CL, clay loam; L, loam; S, sand; SL, sandy loam; SCL, sandy clay loam; SiC, silty clay; SiL, silt loam; SiCL, silty clay loam.

2.2. Cultivated field densities

To develop water content versus strength relationships at densities typical of cultivated soils, surface soil from the Cecil, Houston Black, Sharpsburg and Val- entine was passed through a 2 mm sieve, wetted with a spray bottle, and mixed to various uniform water contents. These soils were chosen to represent a wide

202 L.N. Mielke et al. /Soil & Tillage Research 31 (1994) 199-209

range of clay contents. The soils were then packed to various densities (repre- sentative of field conditions) in a stainless steel conduit 15 cm long with a 25 cm inside diameter. A Bush Recording Soil Penetrometer (Findlay, Irving Ltd., Pen- icuik, UK) fitted with a cone tip 1.2 cm in diameter at its widest point was used to determine the soil strength at the 4.5 cm depth in the column. Ten penetrometer readings were made on each soil column. Plywood 1.2 cm thick, with ten holes 1.3 cm in diameter, was used as a guide for the penetrometer to insure that readings were taken in the same pattern for all the columns and at the same dis- tances from the conduit wall. The ten penetrometer readings were averaged and multiplied by the appropriate factor (151.71 × l0 -3, supplied by the manufac- turer), to estimate the soil strength in MPa for a given soil.

After viewing graphs of the data, it was decided to use two equations of the power function form to describe the relationships of soil water content versus soil strength.

The first equation was

Om= l - o t T / 3 T>~O (1)

where 0m is the fraction of soil water by weight (kg kg-t ), a is a parameter, characteristic of soil (MPa) - #, T is soil strength (MPa), fl is a parameter, characteristic of soil (dimensionless).

The second equation was

Om=3'T -'~ T > 0 (2)

where 3' is a parameter (MPa) ~, ~ is a parameter, characteristic of soil (dimensionless) and T is soil strength (MPa).

The parameters a , fl, 7, and 6 of Eqs. ( 1 ) and (2) were determined using nonlinear least squares regression techniques (Statistical Analysis Systems Institute Inc., 1989). Initial values for iterations can be determined by assuming T > 0 and taking the logto of Eq. (2) to provide

log0,, = log3'- b'log T ( 3 )

which is a straight line with an intercept oflog7 and a slope of - 6 . However, using initial values of 0.5000 for ot and 3' and 0.0100 for fl and ~ resulted in stable values of the parameters of both equations within ten iterations.

For the PT densities, a correlation analysis was made between each of the parameters a, fl, 7, and ~ for fractions of sand, silt, clay, and organic carbon.

3. Results and discussion

3.1. Proctor Test densities

Values of the parameters a and fl of Eq. 1, and 3' and ~ of Eq. 2 at PT densities, are given in Tables 2 and 3 with their standard errors, equation residual mean squares (RMS), and r 2. The r 2 is for a linear regression of predicted versus actual

L.N. Mielke et aL /Soil & Tillage Research 31 (1994) 199-209 203

Table 2 Estimates, standard error, and residual mean squares (RMS) of fitted coefficients c~ and fl of Eq. ( 1 ) for soils or Proctor Test densities. The r 2 is for a linear regression of predicted vs. actual values of soil water content (0) on a mass basis

Soilseries Bulk dens. Soil cr SE fl SE RMS r 2 range layer (X10 -3) ( X 1 0 -3) ( X I 0 5) (Mg m -3)

Crider 1.54-1.61 1 0.7674 6 0.0291 5 4 0.94 1.49-1.66 2 0.7516 9 0.0468 7 15 0.93

Miami 1.66-1.76 1 0.8022 7 0.0311 5 8 0.93 1.67-1.74 2 0.7914 5 0.0333 4 4 0.96

Valentine 1.77-1.83 1 0.8576 11 0.0238 7 9 0.85 1.69-1.78 2 0.8616 10 0.0458 7 20 0.91

Yolo 1.56-1.68 1 0.7764 11 0.0385 8 14 0.88 1.60-1.69 2 0.7702 4 0.0352 4 2 0.97

KoleKole 1.32-1.37 1 0.6138 13 0.0451 10 17 0.92 Caribou 1.47-1.56 1 0.7307 11 0.0401 8 17 0.90

1.35-1.39 2 0.6534 11 0.0487 10 11 0.93 Walla Walla 1.53-1.63 1 0.7858 9 0.0226 6 6 0.89

1.51-1.70 2 0.7708 12 0.0365 7 13 0.87 Barnes 1.50-1.58 1 0.7552 8 0.0304 6 6 0.92

1.61-1.63 2 0.7744 7 0.0343 6 4 0.95 Clarion 1.67-1.77 1 0.8158 9 0.0244 6 6 0.89

1.65-1.73 2 0.7817 8 0.0413 6 4 0.96 Pullman 1.60-1.69 1 0.7850 2 0.0319 2 < 1 0.99

1.48-1.58 2 0.7219 12 0.0572 9 2 0.95 Sharpsburg 1.46-1.55 1 0.7202 14 0.0631 10 22 0.89

1.49-1.54 2 0.7032 7 0.0728 6 11 0.96 Wahiawa 1.26-1.47 1 0.6571 10 0.0489 7 13 0.94 Mohave 1.73-1.90 1 0.8418 5 0.0218 4 4 0.95

1.74-1.93 2 0.8572 5 0.0197 3 3 0.94 Fort Collins 1.58-1.75 1 0.8040 8 0.0367 5 10 0.93

1.61-1.79 2 0.7935 10 0.0374 6 9 0.92 Frederick 1.45-1.54 1 0.7217 23 0.0588 14 52 0.89

1.63-1.73 2 0.7831 5 0.0317 3 2 0.98 Cecil 1.59-1.67 1 0.8000 19 0.0375 11 21 0.79

1.43-1.52 2 0.6895 11 0.0533 9 11 0.92 Rains 1.55-1.64 1 0.7634 12 0.0323 7 19 0.88

1.64-1.76 2 0.8161 4 0.0193 2 1 0.97 Houston Black 1.41-1.53 I 0.6949 10 0.0689 8 5 0.96

1.30-1.43 2 0.6782 3 0.0704 3 3 0.99

values of 0 m. The RMS for the two equations associated with a soil series and layer appear similar. The RMS values of Eq. 1 range from less than 1 × 10- 5 to 5 2 × 10 -5, while values for Eq. 2 ranged from less than 1 × 10 -5 to 6 7 × 10 -5. Smaller RMS values for the chosen Vertisol and Aridisol soils indicate that the equations are better suited for describing soil water content versus soil strength relationships in these soils than for the chosen Oxisol and Spodosol soils which

204 L.N. Mielke et aL / Soil & Tillage Research 31 (I 994) 199-209

Table 3 Estimates, standard error, and residual mean squares (RMS) of fitted coefficients 7 and 6 of Eq. (2) for soils of Proctor Test densities. The r 2 is for a linear regression of predicted vs. actual values of soil water content (0) on a mass basis

Soil series Bulk dens. Soil 7 SE 6 SE RMS r 2 range layer ( X 10 -3 ) ( X 10 -3 ) ( X 10 -5) ( M g m -3)

Crider 1.54-1.61 1 0.2330 8 0.1089 22 5 0.92 1.49-1.66 2 0.2496 11 0.1836 29 20 0.91

Miami 1.66-1.76 1 0.1976 9 0.1520 29 11 0.90 1.67-1.74 2 0.2097 7 0.1551 21 6 0.94

Valentine 1.77-1.83 1 0.1433 13 0.1783 54 11 0.83 1.69-1.78 2 0.1361 12 0.4122 85 29 0.87

Yolo 1.56-1.68 1 0.2254 14 0.1678 37 16 0.87 1.60-1.69 2 0.2321 5 0.1440 17 3 0.96

KoleKole 1.32-1.37 1 0.3874 15 0.0855 20 21 0.90 Caribou 1.47-1.56 1 0.2702 13 0.1335 27 20 0.89

1.35-1.39 2 0.3489 13 0.1107 24 13 0.91 WallaWalla 1.53-1.63 1 0.2154 11 0.0971 26 6 0.87

1.51-1.70 2 0.2331 16 0.1615 33 16 0.84 Barnes 1.50-1.58 1 0.2449 9 0.1071 25 8 0.90

1.61-1.63 2 0.2281 7 0.1439 24 4 0.95 Clarion 1.67-1.77 1 0.1851 11 0.1283 34 7 0.87

1.65-1.73 2 0.2235 12 0.1970 35 7 0.94 Pullman 1.60-1.69 1 0.2187 3 0.1460 11 <1 0.99

1.48-1.58 2 0.3055 20 0.2373 36 1 0.96 Sharpsburg 1.46-1.55 1 0.2848 21 0.2259 42 32 0.84

1.49-1.54 2 0.3044 9 0.2447 23 13 0.95 Wahiawa 1.26-1.47 1 0.3475 13 0.1213 19 15 0.89 Mohave 1.73-1.90 1 0.1585 67 0.1386 27 5 0.93

1.74-1.93 2 0.1443 67 0.1484 25 4 0.92 Fort Collins 1.58-1.75 1 0.1983 11 0.1984 34 14 0.89

1.61-1.79 2 0.2087 14 0.1865 39 15 0.88 Frederick 1.45-1.54 1 0.2812 30 0.2128 56 67 0.77

1.63-1.73 2 0.2195 7 0.1451 19 4 0.97 Cecil 1.59-1.67 1 0.2050 24 0.2039 62 24 0.76

1.43-1.52 2 0.3134 13 0.1477 27 13 0.90 Rains 1.55-1.64 1 0.2078 13 0.1576 36 21 0.86

1.64-1.76 2 0.1851 5 0.1016 13 2 0.97 Houston Black 1.41-1.53 1 0.3176 17 0.2235 34 9 0.93

1.30-1.43 2 0.3266 4 0.2022 9 3 0.99

have higher RMS values. The wide range of RMS values for the chosen MoUisols and Ultisols indicate mixed success of the equations.

The r 2 for Eq. 1 ranges from 0.79 for the Cecil to 0.99 for Houston Black and from 0.76 to 0.99 for Eq. 2. A calculation of correlation coefficients (not in- eluded) indicates that 27% of the variation in a is associated with clay content, and 36% with sand content. For 7, 26% of the variation is associated with clay

L.N. Mielke et al. / Soil & Tillage Research 31 (1994) I99-209 205

content and 36% with sand content. There were no significant correlations between p or 8 with sand, silt, clay or organic carbon content of the soils.

Soil water at various soil strengths determined from the Proctor tests are plotted in Fig. 1. In most cases, because the range in bulk densities is not large for

01 0,3

0,2

0,1

0,0

• Layer 1 Meaured Values o Layer 2 Meaured Values - - Layer 1 Model ........ Layer 2 Model

WaUa WaUa Barnes Clarion

°i Jl 0.3 q

0.2 ~ . ~

o.0 Pullman j ~ Shaq~btttg Valentine °I 0.3

0.2

o.1 ............ ~ .................... s . - b

.., o~,,,o J l ~ ° ' Y ° ' ~ o.o -~, . . . . . . . .

o.o - ~ . , . , - ~

l .<. 0.3 c, ....Q

0.2

; o 0.1

. . . . lli o ....

Yolo

010203 o I ii • Kole Kole Wahiawa ~ ~ b o u

0 . 0 , ,-- , , . . . . . .

0 6 12 18 0 6 1'2 18 0 6 12 18

Soil Strength (MPa)

Fig. 1. Water content of 18 benchmark soils as a function of soil strength at Proctor Test (PT) densities. Differences in the curves f rom the two equations were visually indistinguishable at this scale so

Eq. 1 was used to plot the curves.

206 L.N. Mielke et al. ~Soil & Tillage Research 31 (1994) 199-209

m o s t soi ls , t h e r e is a r e l a t i v e l y s m a l l a d v e r s e effect o f b u l k d e n s i t y o n the fi t o f t he e q u a t i o n s to t he da t a . A l t h o u g h the r 2 va lue s were s l ight ly h i g h e r for Eq. 1, t he cu rves p r e d i c t e d b y the two e q u a t i o n s d i f f e r e d on ly s l igh t ly for m o s t soi ls a n d c o u l d n o t be v i sua l l y d i f f e r e n t i a t e d f r o m t h e s ize o f t he g r a p h s in Fig. 1 ( d a t a n o t s h o w n ) . T h u s , t he cu rves in Fig. 1 were d r a w n us ing Eq. 1.

3.2. Cultivated f i e ld densities

Values o f t he soi l c h a r a c t e r i s t i c p a r a m e t e r s a a n d fl o f Eq. 1, a n d 7 a n d 5 o f Eq. 2 for fou r so i l s a t c u l t i v a t e d f ie ld ( C F ) dens i t i e s , a r e g iven in T a b l e s 4 a n d 5 wi th

Table 4 Estimates, standard error, and residual mean squares (RMS) of fitted coefficients c~ and fl of Eq. ( 1 ) for cultivated field densities of surface soils. The r 2 is for a linear regression of predicted vs. actual values of soil water content (0) on a mass basis

Soil series Bulk dens. c~ SE fl SE RMS r 2 range (X l0 -3 ) (X l0 -3) (Xl0 -5 ) (Mgm -3)

Valentine 1.28-1.45 0.6574 23 0.0531 8 32 0.86 1.28-1.30 0.5244 177 0.0968 64 118 0.69 1.34-1.36 0.6822 20 0.0447 7 12 0.94 1.28-1.36 0.6646 29 0.0512 9 38 0.83

Sharpsburg 1.00-1.30 0.4101 62 0.1026 26 282 0.66 1.10-1.15 0.3187 115 0.1380 60 500 0.74 1.25-1.30 0.4447 25 0.0911 10 27 0.96

Cecil 1.00-1.35 0.5366 132 0.0806 53 169 0.31 Houston Black 1.11-1.59 0.2626 45 0.1607 28 421 0.67

1.20-1.23 0.2385 44 0.1743 29 153 0.88 1.30-1.31 0.3304 94 0.1295 47 384 0.71

Table 5 Estimates, standard error, and residual mean squares (RMS) of fitted coefficients y and 5 of Eq. (2) for field densities of surface soils. The r 2 is for a linear regression of predicted vs. actual values of soil water content (0) on a mass basis

Soil series Bulk dens. 7 SE 5 SE RMS r 2

range (x10 -3) (×10 -3 ) (X10 -5) (Mgm -3)

Valentine 1.28-1.45 0.4534 76 0.2294 4 45 1.28-1.30 2.6033 6787 0.5773 51 149 1.34-1.36 0.3878 50 0.1913 3 16 1.28-1.36 0.4332 86 0.2233 5 51

Sharpsburg 1.00-1.30 1.4467 776 0.3071 8 254 1.10-1.15 2.0866 1137 0.3518 12 367 1.25-1.30 1.1108 305 0.2669 5 59

Cecil 1.00-1.35 0.8199 744 0.2849 20 17 Houston Black 1.11-1.59 1.9445 726 0.3135 7 513

1.20-1.23 2.7586 1250 0.3682 8 229 1.30-1.31 1.6975 1409 0.3060 15 474

0.80 0.61 0.91 0.78 0.70 0.81 0.92 0.31 0.60 0.83 0.64

L.N. Mielke et aL/ Soil & Tillage Research 31 (1994) 199-209 207

0.0 +::[ 0.2

~ ° ' l t H o u s t o n B l a c k

• i . , . , . i . , . , .

° ' ° .0 0.2 0.4 0.0 0.0 1 . o 1 +2 1 . 4

So i l S t r e n g t h ( M P a )

o.e

~ 0.0 o

0.2

~ o.1

° '~ . o

- - r " s 0 . 8 9

. . . . ra = 0.71 .~ - - 0 1.20 - 1.23 Mo+m ~ ~ . ~ . . . . 0 1.30 - 1.31 Mg.m ~ 0 " ; ~ . 0

o ~ ' ~ ' ~ ' . . ~ ~

Houo ton Blsek

o12 ' o14 ' 0.'+ ' oi, 12o , . ' 2 " ,., Soil Strength (MPa)

~ O.E

i 0.4

0 . 3

0.2

0.1

0 , 0 . 0 '

P = 0.86

S h o r l ~ b u r g

o'.= ' 0 ' . , ' o'.0 ' 0 ' . 0 1.0 ,~ Soil Strength (MPa)

o . e i

~ O.lS

~ o-,I o

~o. , I

o.o' 1.4

- - r ' = 0.74 . . . . P - 0.86

, 0 - - - 0 1.10 - 1.15 Mg.m ~ . . . . 0 1.25 - 1 +30 Mo.m a

< + ' ~ ' " " o o ...... .'~7~.~... ""0~ . . . . . . . . . . . . . . . . 0 . .

Shorpsburg

0.2 0.4 0.0 0.8 1.0 1.2

Soil Strength (MPa)

0 . 3 2

. ~ 0.24

O.le

U

o.o|

~ r t = O.B6

e

V a l e n t i n e

0 . ~ . + . o . ~ " 0.;0 " 0 . ' , , , " o.~. " o . ~ " o . ~ Soil Strength (MPa)

c s 0.24

o+1~ o

(.)

o.oo

- - p = 0 , 8 4 . . . . i - , = 0 . 9 4 - - r" = 0 . 8 9

~ % ~ . ---- 0 1.28 - 1.30 Me.m s . . . . 0 1.34 - 1.36 Mo.m 4

1.28 - 1.36 Mo.rn "a

o

Va len t ine

o. • " ' • ' " ' - ' • ' °~.00 0.06 0.10 0.16 0,20 0.26 0.30


0 . 3 , 1

0.24

o.1~

+

~ o . o I

o,o~.

i ~ a 0 . 3 1

Ceoll

t ~ . . 0.10 o. 6 0.20 0.25 0.30


Fig. 2. Water content of four soils (surface layer) as a function of soil strength at various cultivated field (CF) densities. Differences in the curves from the two equations were visually indistinguishable at this scale so Eq. ( 1 ) was used to plot the curves. The left side of the figure contains curves for the full range of densities while the right side contains curves for indicated density ranges.

208 L.N. Mielke et al. ~Soil& Tillage Research 31 (1994) 199-209

their standard errors, equation RMS, and r 2. Because soil density changes in the CF range seem to have a greater effect on soil strength than those in the PT range, data in Tables 4 and 5 are grouped by various bulk density ranges. For Cecil soils, it was apparent from the scatter of the data that separating these data into several ranges would not improve either the r 2 or RMS values for this soil. Therefore, the parameters of Eqs. 1 and 2 are presented for one bulk density range for the Cecil Sandy Loam.

The RMS values ofEq. 1 ranged from 12)< 10 -5 to 500× 10 -s. RMS values for Eq. 2 ranged from 16× 10 -5 to 513)< 10 -5. The r z values ranged from 0.31 to 0.96 for Eq. 1 and from 0.31 to 0.91 for Eq. 2, the 0.31 being that for the Cecil. Smaller RMS values and larger r 2 values for density ranges of 1.34-1.36 Mg m -3 for the Valentine and 1.25-1.30 Mg m - 3 for the Sharpsburg soil indicate that both equations are better suited for describing soil water content versus soil strength relationships for these soils. However, these equations are less suitable for describing soil water content versus soil strength relationships for Houston Black clay and not very good for the Cecil Sandy Loam. The wide range of RMS values indicates a mixed success in using the equations for the chosen soils and density ranges.

Soil water content at various soil strengths determined at CF densities for the Valentine, Sharpsburg, Cecil and Houston Black soils are plotted in Fig. 2. As in Fig. 1, the curves in Fig. 2 were drawn using Eq. 1. The left side of Fig. 2 contains curves for the full range of densities while the right side contains curves for various density ranges. Because soil strength increased with decreasing soil water content to a maximum and then decreased sharply at lower water content, data at these lower water contents were not used in Fig. 2. Thus, caution must be taken not to extend the curves beyond the data points shown for a given curve. It is for this reason that some of the curves in Fig. 2 do not cover the entire range of soil strengths shown on the horizontal axis.

4. Summary and conclusions

Both regression equations adequately predicted soil water content from soil strength measurements obtained at PT densities. However, r 2 and RMS values are slightly better for Eq. 1 than Eq. 2. When applied to soils at CF densities, Eqs. 1 and 2 have lower r 2 values and higher RMS. This difference is possibly due to the wide range in CF bulk densities resulting in more scatter of data. Only 36% of the variation in equation parameters at PT densities were explained by sand content.

Soil strength at cultivated field bulk densities can undergo abrupt changes at very low water contents. Thus, some of the data should not be used to determine curve parameters. The relationship between soil water content and soil strength also changes abruptly as the soil becomes water saturated. Therefore, caution must be exercised in using these equations for very wet and very dry soils and curves must not be extended beyond the data points used to determine equation param-

L.N. Mielke et al. ~Soil & Tillage Research 31 (1994) 199-209 209

eters. For some bulk density ranges and soils, the equations appear to have prom- ise as a means of estimating soil water content during field operations. Such real time data would be useful when applying variable rate application technology.

Acknowledgments

The authors gratefully acknowledge Janice Gion and Gary Wieman for their data analysis and preparation of the figures and the National Soil Mechanics Lab- oratory and the National Soil Survey Laboratory staff of the US Soil Conserva- tion Service, Lincoln, NE for running the Proctor density tests and determining the soil characteristics in Table 1.

References

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estimating soil water content from soil strength

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