United States Department of Agriculture United States Department of Agriculture - Agricultural Research Service Agricultural Research Service
Northwest Irrigation & Soils Research Lab,  Kimberly, ID

Soil Strength Relationships of a Durinodic Xeric Haplocalcid Soil

R.E. Sojka*, W.J. Busscher1 and G.A. Lehrsch2

*Send comments on this poster to the corresponding author: Bob Sojka

*2Soil Scientists, USDA Agricultural Research Service, Kimberly, ID
1Soil Scientist, USDA Agricultural Research Service, Florence, SC


For most soils, strength depends mostly on the interaction of water content (WC) and bulk density (BD).  We hypothesized that soil strength (cone index, or CI) of an important Pacific Northwest (PNW) soil, Portneuf silt loam (Durinodic Xeric Haplocalcid), could be predicted for a given BD or WC, and would increase with increasing BD and decreasing WC.  To test this, CI, BD and WC profile of a Portnuef soil in a 1.5-ha field was intensively sampled three times in two years, producing 688 data triplets that were used to produce WC-CI-BD response-surface relationships.  Relationships were poor when derived from full-profile data sets but improved when data were segregated by depth.  CI of individual layers were always strongly correlated with WC, but not always with BD.  High CaCO3 content of this soil may have produced cementation effects that varied with prolonged wetting vs. prolonged drying.  Variability among in situ CI penetrations and BD corings also reduced model accuracy.  The difficulties in developing comprehensive relationships of CI to BD, and the dependency of CI on WC, suggest great uncertainty in using BD for sensitive assessment of soil status affecting root restriction or crop performance, unless sampling is extensive and the relationships between CI, BD, and WC are intensively documented for specific horizons of an individual soil.


Few published CI/soil-property relationships have been derived from in situ measurements.  Most are from soil cores prepared under laboratory conditions or from undisturbed cores brought into the laboratory.

To measure in situ CI, one commonly uses various types of recording ASAE standard cone penetrometers.  Still, in situ CI is rarely reported with WC at the time of measurement or with calibration to or assessment of other in situ properties because of intensive labor requirements.


No in situ CI-BD-WC relationships were available for Durinodic Xeric Haplocalcid soils, which occupy large areas of the PNW and are highly productive but compaction-prone.  To relate CI to BD and WC, we intensively sampled a 1.5-ha field of Portneuf silt loam three times in two years, with the hypothesis that CI would increase with increasing BD and decreasing WC.  We were also interested in determining whether that relationship differed with soil depth.

Materials & Methods

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The experiment was conducted from 1988 through 1990 on a field of Portneuf silt loam (coarse silty, mixed, superactive, mesic Durinodic Xeric Haplocalcid) near Kimberly, ID, USA.  The Portneuf soil, formed in loess, has a calcium carbonate- and silica-enriched B horizon.  Profile soil properties are in Table 1.

Table 1.  Portneuf silt loam properties, sampled 290 m from study site (McDole and Maxwell, 1987).
  Partical Size Distribution  
Horizon Depth Sand Silt Clay Bulk Density Org. C CEC pH 1:1 water EC CaCO3 equiv.
  cm % % % g cm-3 g kg-1 cmolc kg-1   S m-1 %
Ap 0-28 14 66 20 1.48 10 18.6 8.0 0.07 2
Bk 28-58 8 71 21 1.45 6 13.7 8.4 0.05 24
Bkq1 58-102 16 80 4 1.43 4 11.7 8.5 0.05 21
Bkq2 102-137 18 81 1 1.42 2 12.7 8.5 0.05 16

At initiation of this study, in 1988 and 1989 the complete site was in corn (Zea maze L.).  Natural variation at sampling due to irrigation, crop uptake, and over-winter precipitation provided the range in WC among samples.
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BD and CI were measured three times: 26 Apr to 9 May 1988 after fall moldboard plowing and spring secondary tillage; 25-28 Oct 1988 after corn harvest but before fall tillage; and 9-12 Apr 1990 in undisturbed stover from the 1989 corn crop.  Data from these three samplings were used to determine BD-CI-WC relationships.

Soil samples were taken from 0 to 60 mm depth in Spring 1988 at each sampling site using a 54-mm diameter hand coring tool.  In Fall 1988 and Spring 1990, samples were taken from 0 to 35 mm using a 51-mm diameter hand coring tool.  At each site, subsoil samples were obtained from a 32-mm core taken with a tractor-mounted hydraulic soil probe.  Triplicate surface samples were taken at each sampling site, separating subsamples by 15 cm to avoid compaction from neighboring corings.  Surface and subsoil samples were taken between the wheel tracks of the tractor.  Subsoil corings were offset from surface sampling areas to avoid measurement artifacts.

Subsoil cores were sampled by depth, after ensuring that no surface compaction had occurred.  Subsoil samples were 0.15 to 0.30, 0.30 to 0.45, and 0.45 to 0.60 m.  For the surface depth increment of each sampling site, CI was matched with the average BD and WC of the three surface samples.

Click here to view a bigger image of the recording penetrometer. Then use your browsers Back button to return here. Click here to view a bigger image of the CI-trace digitizing process. Then use your browsers Back button to return here.
After each coring, profile CI was measured using a hand operated recording cone penetrometer (standard ASAE 13-mm diameter, 30o solid angle cone).  Three penetrations were made 15 to 20 cm down the row from each core along the non-wheel-track mid row.  The penetrometer recorded CI to the 0.60-m depth.  CI values at 5-cm depth increments for each of the three traces were averaged to give a single value.  WCs, taken at 15-cm depth intervals, were associated with corresponding CIs.

Mean CIs were regressed against the mean BD and/or gravimetric WC for all depths together and for selected depth increments.  We used a curve fitting procedure that considered thousands of possible equations using TableCurve software (SSI, Richmond, CA).

We interpreted the data via regression analyses.  Equation forms examined for best fit included higher powers of x and y and use of log and semi-log relationships, emphasizing fits with high correlation coefficients, and simple, physically reasonable curve forms.  We ignored fits that were merely tortuous adaptations to the data.  Outliers regarded as physically impossible were deleted.  Of 688 data triplets, only 35 were excluded; 25 of which were due to off-scale high CIs and 10 from ultra low readings believed caused by buried cracks or macropores.

The equations retained and presented in tables met the assumption of normally distributed residuals.  This same protocol was used to examine a variety of two-independent-variable relationships with volumetric water content and CI.  The 3-D relationships produced poorer fits than using only gravimetric water content and CI.  Volumetric water content and BD cannot both be used as independent variables since BD is represented both as a separate parameter and as part of the volumetric WC variable.

Results & Discussion

Mean BDs, CIs, and WCs as a function of depth (Table 2) show that wide ranges of compaction and field water status were encountered among sampling times and depths.

Table 2.  Mean and standard deviations (sd) for bulk densities (BD), water contents (WC), and soil strengths (CI) for the various dates of measurement.
April '88
depth BD sd WC sd CI sd
m g cm-3 g g-1 MPa
0-0.08 1.15 0.06 0.122 0.023 0.19 0.21
0.15-0.30 1.32 0.08 0.176 0.017 0.87 0.54
0.30-0.45 1.53 0.06 0.183 0.024 4.96 1.47
0.45-0.60 1.57 0.05 0.160 0.026 4.05 3.07
October '88
depth BD sd WC sd CI sd
m g cm-3 g g-1 MPa
0-0.08 1.24 0.06 0.073 0.013 0.62 0.57
0.15-0.30 1.33 0.08 0.117 0.020 3.58 0.17
0.30-0.45 1.5 0.04 0.118 0.038 7.55 1.55
0.45-0.60 1.53 0.05 0.107 0.036 8.51 0.52
April '90
depth BD sd WC sd CI sd
m g cm-3 g g-1 MPa
0-0.08 1.15 0.07 0.070 0.012 0.22 0.10
0.15-0.30 1.44 0.16 0.148 0.009 0.75 0.28
0.30-0.45 1.55 0.20 0.192 0.017 3.91 1.35
0.45-0.60 1.53 0.05 0.178 0.020 8.06 1.51

We did not assume a single curve form would fit the data.  All equations producing good fits were considered.  The simplest curve with the highest R2 was chosen.  Usually only a few simple curve forms met the data and screening criteria.  If R2 values were similar among curve forms, the simplest curve was chosen.  If curves had similar complexity but varied in R2, the form with the highest R2 was chosen.

Mean CIs for all BD sampling intervals were initially regressed against WC and BD, using data from all depths (Table 3).  The R2 of 0.45 prompted analyses by depth increments (Table 3).

Table 3.  Evaluation of fit of three dimensional and two dimensional regression with regression coefficient (R2) and standard error (se).  Three dimensional fits regress mean soil strength (MPa) against both water content (g g-1) and bulk density (g cm-3).  Two dimensional fits regress soil strength against water content.
Mean Strength (MPa)
  Three Dimentional Two Dimentional
Depth (m) R2 se n R2 se n
0-0.08 0.05 0.23 174 0.05 0.28 174
0.15-0.30 0.60 0.59 170 0.68 0.53 170
0.30-0.45 0.42 0.98 144 0.38 1.00 144
0.45-0.60 0.09 3.06 165 0.03 3.17 165
all depths 0.45 2.14 653 0.10 2.73 653

Figure 1. CI-WC-BD relationship. Click here to view a bigger image of Figure 1. Then use your browsers Back button to return here.
CI-BD-WC regressions using all triplets (Fig. 1, Table 4) revealed that CI increased sharply with increasing BD (slope = 10.9 MPa cm3 gs-1) but decreased only slightly with increasing WC (slope = -0.11 MPa gs gw-1) (gs = grams of soil and gw = grams of water).

Portneuf soil often has only a shallow Ap horizon and pronounced zones of high BD below it.  Thus, we segregated data by depth intervals.  BD was determined separately for the 0-0.08, 0.15-0.30, 0.30-0.45, and 0.45-0.60 m depth intervals.  The relationships for the 0.15-0.30 and 0.30-0.45 m depth intervals were as good as or better than the overall profile (Table 3).  However, the relationships for 0-0.08 m and 0.45-0.60 m showed almost no CI dependence on BD or WC.

The low surface BDs in April 1988 and 1990 (Table 2) revealed that the surface soil was without a cohesive matrix, which in turn prevented the kinds of matrix effects necessary to produce WC- or BD-related CI changes.  At deeper depths, insensitivity arose from the penetrometer's inability to smoothly penetrate caliche subsoil, frequently reaching its maximum recordable value.

Although CI was affected more by changes in BD than WC for the entire data set (Fig. 1), this was not true when the data were analyzed by depth.  For the 0.15-0.30 and 0.30-0.45 m depths, WC alone often explained as much or even more variation in CI than the combination of BD and WC (Table 3).  The variation of BD at a given depth was probably less than the variation of WC.

For the 0.15-0.30 m depth, the best 3-D fit produced R2=0.60 (Table 3).  While this was an improvement over the full profile data set, an R2 of 0.68 was obtained for mean CI vs. WC, using a simple power function (Table 4).  Figure 2 shows that CI could be predicted reasonably well with WC alone, especially for discreet depths.

Figure 2. CI-WC relationship at two depths. Click here to view a bigger image of Figure 2. Then use your browsers Back button to return here.
For the 0.30-0.45 m depth, the best 3-D fit produced R2=0.42 (Table 3).  The same kind of 2-D power function used for 0.30-0.45 m produced R2=0.38.  The addition of BD did not improve the regression.

Combining depths gave poor regressions.  The individual regressions of depths and their scatter (Fig. 2, Table 4) show why combining layers can give erroneous predictions of CI as a function of WC, and make a strong case for individual depth-specific regressions.  In this calcareous soil, WC is a good CI predictor in the BD range common in field cropping, if the WC calibration to CI is depth-specific (or horizon specific).

Table 4.  Equations used for the regression calculations.  Equation forms and constants used to produce the data in Table 2, where z=cone index (MPa), x=water content (g g-1) and y=bulk density (g cm-3).
  Three Dimensional Two Dimensional
Depth (m) Equation a b c Equation a b
0.15-0.30 z=a+bx-1+cy -2.29 66.6 -0.56 z=axb 0.0003 -3.16
0.30-0.45 z=a+bx-1+cy -1.44 117 -0.42 z=a+bx 11.8 -0.37
All depths z=a+bx+cy -12.1 -0.11 10.9 z=a+bx 0.78 0.23


Portions of these data, when segregated by depth, show sensitivity of soil strength to the combined influence of water content and bulk density.  However, more often than not, in situ-determined soil strength as CI was equally or more sensitive to water content alone.

These data from a Durinodic Xeric Haplocalcid may represent a situation where calcium carbonate and cementation play a significant role in soil strength response to WC.

The number of samples in this study was very large.  Yet, robust correlations were difficult to obtain.  This should serve as a caution against using sparse numbers of bulk density or soil strength measurements to interpret soil status (so-called "soil quality").

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