Article Figures & Data
Figures
- Figure 1.
Schematic details of an inflatable rubber diaphragm to provide a laboratory simulation of a tree root. The image was adapted from AutoCad fabrication details (Cook agricultural engineering shop). Photo inset shows the “root” inflated at low pressure for demonstration purposes.
- Figure 2.
Schematic drawing of the testing system with diaphragm, box, root, and pad. The box was designed to accept nesting sidewalls to adjust the distance from “root” to a pressure mapping pad recessed in the box top. The lower insets provide aspect ratios between the “root” and the mapping pad. The top left photo shows the load cell pad recessed in the box top, while the right upper photo shows the testing box with five lifts over the root. The inlet for pressurized water is shown in the center of the base wall. The box top was marked with the load cell grid to track signals with relation to the root when testing was in progress.
- Figure 3.
Example of a root calibration sequence that included a mapping signal regression between input manifold pressure and load cell output when the root was in direct contact with the load cell pad. The computer tomography and raw signal data used to create the tomograph and calibration regression relationships are shown at right of the calibration regression plot.
- Figure 4.
Characterization of the testing sand used in the example study, a USCS SP medium fine sand.
- Figure 5.
a) A data plot showing load cell mean output in a moderately compacted sand (1.63 Mg m−3) at medium (6%) gravimetric moisture. Mean sensor readout (n = 8) in kPa for line loads parallel to the inflating root at an inflation pressure of 400 kPa. Sensor readout developed from 30 second measurements collected at 38 Hz. b) The associated pressure-yield curve with best-fit polynomial curve shown y = −0.0000001x3 + 0.000271x2 + 0.01662x + 0.916 R2 = 0.76. The circled values show displacements at 400 kPa which link the load cell output to the pressure-yield curve data. Square data points show sigmoid character of an individual testing run.
- Figure 6.
a) A data plot showing load cell mean output in a compacted sand (1.71 Mg m−3) at low (0.08%) gravimetric moisture. Mean sensor readout (n = 8) in kPa for line loads parallel to the inflating root at an inflation pressure 400 kPa. Sensor readout developed from 30 second measurements collected at 38 Hz. b) The associated pressure-yield curve with best-fit polynomial curve shown y = 0.0000005x3 − 0.000279x2 + 0.09127x + 0.0386 R2 = 0.91. The circled values show displacements at 400 kPa, which link the load cell output to the pressure-yield curve data.
Tables
- Table 1.
Best fit polynomial regression pressure-displacement curves for a sand compacted to different densities at low (<1%), medium (6%), and high (12%) gravimetric moisture content.
Sand density Mg m−3 Gravimetric moisture Equation
y =displacement volume (cm3)
x = input pressure (kPa)R2 Model p value 1.51 0.10% y = −0.0000047x3 + 0.002191x2 + 0.14722x − 0.0776 0.86 <0.001 1.71 0.08% y = 0.0000005x3 − 0.000279x2 + 0.09127x + 0.0386 0.91 <0.001 1.64 0.10% y = 0.0000003x3 + 0.00009x2 + 0.02973x + 0.6384 0.97 <0.001 1.63 6.00% y = −0.0000001x3 + 0.000271x2 + 0.01662x + 0.916 0.76 <0.001 1.67 12.00% y = 0.0000008x3 − 0.000312x2 + 0.06401x − 0.3949 0.92 <0.001 - Table 2.
Testing output versus the expected polynomial regression model sand displacements at input level 400 kPa. Low, medium, and high descriptors were used to distinguish intended treatment levels. XX = Input level for density 1.51 that was limited to 350 kPa since sand displacement volumes exceeded measurement capacity and are considered unreliable. Subscripts of different letter for testing output displacement were different at α = 0.05 in Oneway AOV. Testing output was consistent with model outputs in the 400 kPa root inflation pressure.
Sand Density Mg m−3 Gravimetric moisture Observed Displacement (cm3) @ 400 kPa ± Std. error Model Displacement (cm3) @ 400 kPa ± confidence interval a = 0.05 1.51 (low) 0.10% (low) ----- 106 ± 31 XX 1.71(high) 0.08% (low) 23 ± 2a 23 ±1 1.64 (med) 0.10% (low) 48 ± 2b 49 ± 2 1.63 (med) 6.00% (med) 48 ± 7b 43 ± 2 1.67 (high) 12.00% (high) 28 ± 5a 28 ± 1
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