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![Page 1: Eidgenössisches Volkswirtschaftsdepartement EVD Forschungsanstalt Agroscope Reckenholz-Tänikon ART 4a. Mechanical stresses during wheel traffic Thomas.](https://reader036.fdocuments.us/reader036/viewer/2022062511/551a83d85503466b3a8b4905/html5/thumbnails/1.jpg)
Eidgenössisches Volkswirtschaftsdepartement EVD
Forschungsanstalt Agroscope Reckenholz-Tänikon ART
4a. Mechanical stresses during wheel traffic
Thomas Keller1,2, Mathieu Lamandé3, Matthias Stettler4 and Per Schjønning3
1Agroscope Reckenholz-Tänikon Research Station ART, Reckenholzstrasse 191, CH-8046 Zürich, Switzerland; E-mail: [email protected]
2Swedish University of Agricultural Sciences, Department of Soil and Environment, Box 7014, SE-75007 Uppsala, Sweden
3Department of Agroecology, Aarhus University, Research Centre Foulum, P.O. Box 50, DK-8830 Tjele, Denmark
4Swiss College of Agriculture, Länggasse 85, CH-3052 Zollikofen, Switzerland
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2Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
1. Contact tyre/track-soil = Upper model boundary condition: Contact area Stress distribution
2. Stress propagation
0.4
0.5
0.6
0.7
0 0.5 1 1.5 2 2.5 3 3.5
Log stress (kPa)
Vo
id r
ati
o3. Stress-strain (void ratio) relationship &
Mechanical soil strength Stress > Strength Compaction Stress < Strength Elastic deformation
Soil compaction in three steps...
![Page 3: Eidgenössisches Volkswirtschaftsdepartement EVD Forschungsanstalt Agroscope Reckenholz-Tänikon ART 4a. Mechanical stresses during wheel traffic Thomas.](https://reader036.fdocuments.us/reader036/viewer/2022062511/551a83d85503466b3a8b4905/html5/thumbnails/3.jpg)
3Kolloquium FB31 | BodenverdichtungThomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
Stress propagation in soil
![Page 4: Eidgenössisches Volkswirtschaftsdepartement EVD Forschungsanstalt Agroscope Reckenholz-Tänikon ART 4a. Mechanical stresses during wheel traffic Thomas.](https://reader036.fdocuments.us/reader036/viewer/2022062511/551a83d85503466b3a8b4905/html5/thumbnails/4.jpg)
4
Analytical solutions-Simple and robust-3-Dimensional-Limitations:
• Elastic theory
(e.g. Keller & Lamandé 2010, Soil & Tillage Research 111)
Finite element modelling (FEM)-Continuum mechanics-Elasto-plastic stress-strain relationships (e.g. Modified Cam Clay)-Can account for stress-dependent material properties-Limitations:
• Description of tyre-soil contact• Parameterization
(e.g. Richards & Peth 2009, Soil & Tillage Research 102)
Modelling stress propagation
![Page 5: Eidgenössisches Volkswirtschaftsdepartement EVD Forschungsanstalt Agroscope Reckenholz-Tänikon ART 4a. Mechanical stresses during wheel traffic Thomas.](https://reader036.fdocuments.us/reader036/viewer/2022062511/551a83d85503466b3a8b4905/html5/thumbnails/5.jpg)
5
Analytical solutions-Simple and robust-3-Dimensional-Limitations:
• Elastic theory
(e.g. Keller & Lamandé 2010, Soil & Tillage Research 111)
Finite element modelling (FEM)-Continuum mechanics-Elasto-plastic stress-strain relationships (e.g. Modified Cam Clay)-Can account for stress-dependent material properties-Limitations:
• Description of tyre-soil contact• Parameterization
(e.g. Richards & Peth 2009, Soil & Tillage Research 102)
Modelling stress propagation
Suitable for easily-applicable decision support tools Approach in Terranimo®
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7
x
y
z
rѲ
P
σr
cos2
32r
Pr
For elastic material (Boussinesq, 1885):
Stress propagation: point load
Boussinesq J (1885) Application des Potentiels à l’étude de l’équilibre et du Mouvement des Solides Élastiques. Gauthier-Villars, Paris, 30 pp.
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
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8
Soil is not fully elastic… Therefore (Fröhlich, 1934):
2
2cos
2
r
Pr x
y
z
rѲ
P
σr
ν = „concentration factor“ (empirical factor)
Stress propagation: point load
Fröhlich OK (1934) Druckverteilung im Baugrunde. Springer Verlag, Wien, 178 pp.
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
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9
ni
ii
i
iz
z
P
0
22 cos
2
σz
Pi
zi
Stress propagation: Söhne‘s summation procedure
Söhne W (1953) Druckverteilung im Boden und Bodenverformung unter Schlepperreifen. Grundlagen der Landtechnik 5, 49-63.
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
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10Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
(Boussinesq, 1884; Fröhlich, 1934; Söhne, 1953)
Stress propagation in soil
Boussinesq J (1885) Application des Potentiels à l’étude de l’équilibre et du Mouvement des Solides Élastiques. Gauthier-Villars, Paris, 30 pp.
Fröhlich OK (1934) Druckverteilung im Baugrunde. Springer Verlag, Wien, 178 pp.
Söhne W (1953) Druckverteilung im Boden und Bodenverformung unter Schlepperreifen. Grundlagen der Landtechnik 5, 49-63.
ni
ii
i
ir
r
P
0
22 cos
2
ν = Concentration factor
Söh
ne W
(19
53)
Gru
ndla
gen
der
Land
tech
nik
5, 4
9-63
.
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11
0.0
0.2
0.4
0.6
0.8
1.0
0 50 100 150 200 250
De
pth
(m)
Vertical stress (kPa)
Stress distribution at the tyre-soil contact affects stress propagation
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
Simulated, using uniform stress distribution
Measured stress
Simulated, using measured stress distribution
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12
0.0
0.2
0.4
0.6
0.8
1.0
0 50 100 150 200 250
De
pth
(m)
Vertical stress (kPa)
Stress distribution at the tyre-soil contact affects stress propagation
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
?
But…
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13Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
Idea…
?
Model
Stress distribution
Easily-available tyre/loading properties (e.g., tyre dimensions, tyre inflation
pressure, wheel load) and information on soil condition/consistency
![Page 13: Eidgenössisches Volkswirtschaftsdepartement EVD Forschungsanstalt Agroscope Reckenholz-Tänikon ART 4a. Mechanical stresses during wheel traffic Thomas.](https://reader036.fdocuments.us/reader036/viewer/2022062511/551a83d85503466b3a8b4905/html5/thumbnails/13.jpg)
14Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
Measuring stress distribution at the tyre-soil interface
Photos: Per Schjønning68
340
3468
-59-29
029
590
50
100
150
200
250
Ge
me
ss
en
er
Dru
ck
(k
Pa
)
Länge (cm) Breite
...
Fahrtrichtung
1 2
34
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15Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
Tyre: 800/50 R34; Wheel load: 6000 kg
Upper model boundary condition: Model „FRIDA“
Measured
Modelled
Keller T (2005) A model for prediction of the contact area and the distribution of vertical stress below agricultural tyres from readily-available tyre parameters. Biosystems Engineering 92, 85-96.
Schjønning P, Lamandé M, Tøgersen FA, Arvidsson J & Keller T (2008) Modelling effects of tyre inflation pressure on the stress distribution near the soil-tyre interface. Biosystems Engineering 99, 119-133.
Model ‘FRIDA’:(Keller, 2005; Schjønning et al. 2008)
Contact area
Stress distribution
1//|, nnbyaxyx
),(),(),,,,(),( yxgyxfnbaCFyx wheel
)(1),(
yl
xyxf
x
gm
xw
y
xw
yyxg
yy
/)(
1exp)(
1),(
![Page 15: Eidgenössisches Volkswirtschaftsdepartement EVD Forschungsanstalt Agroscope Reckenholz-Tänikon ART 4a. Mechanical stresses during wheel traffic Thomas.](https://reader036.fdocuments.us/reader036/viewer/2022062511/551a83d85503466b3a8b4905/html5/thumbnails/15.jpg)
16
0.0
0.2
0.4
0.6
0.8
1.0
0 50 100 150 200 250
Vertical stress (kPa)
De
pth
(m
)Predicting stress in soil
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
Simulated, using uniform stress distribution
Measured stress
Simulated, using FRDIA generated stress distribution
Simulated, using measured stress distribution
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17Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
1. Contact tyre/track-soil = Upper model boundary condition: Contact area Stress distribution
2. Stress propagation
0.4
0.5
0.6
0.7
0 0.5 1 1.5 2 2.5 3 3.5
Log stress (kPa)
Vo
id r
ati
o3. Stress-strain (void ratio) relationship &
Mechanical soil strength Stress > Strength Compaction Stress < Strength Elastic deformation
Soil compaction in three steps...
![Page 17: Eidgenössisches Volkswirtschaftsdepartement EVD Forschungsanstalt Agroscope Reckenholz-Tänikon ART 4a. Mechanical stresses during wheel traffic Thomas.](https://reader036.fdocuments.us/reader036/viewer/2022062511/551a83d85503466b3a8b4905/html5/thumbnails/17.jpg)
Federal Department of Economic Affairs FDEA
Agroscope Reckenholz-Tänikon Research Station ART
6a. Stress transmission
Thomas Keller1,2, Mathieu Lamandé3, Matthias Stettler4 and Per Schjønning3
1Agroscope Reckenholz-Tänikon Research Station ART, Reckenholzstrasse 191, CH-8046 Zürich, Switzerland; E-mail: [email protected]
2Swedish University of Agricultural Sciences, Department of Soil and Environment, Box 7014, SE-75007 Uppsala, Sweden
3Department of Agroecology, Aarhus University, Research Centre Foulum, P.O. Box 50, DK-8830 Tjele, Denmark
4Swiss College of Agriculture, Länggasse 85, CH-3052 Zollikofen, Switzerland
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19Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
Stress propagation in soil: Simulation vs. measurements (typical result)
Possible reasons (Keller & Lamandé, 2010):
(1) Upper model boundary condition is wrong
(2) Model for stress propagation is inappropriate
(3) Stress measurements are inaccurate
Keller T & Lamandé M (2010) Challenges in the development of analytical soil compaction models. Soil & Tillage Research 111, 54-64.
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20Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
Stress propagation in soil: Simulation vs. measurements (typical result)
Possible reasons (Keller & Lamandé, 2010):
(1) Upper model boundary condition is wrong
(2) Model for stress propagation is inappropriate
(3) Stress measurements are inaccurate
Keller T & Lamandé M (2010) Challenges in the development of analytical soil compaction models. Soil & Tillage Research 111, 54-64.
FRIDA
1) We know that we are within 10% (Lamandé et al., unpublished)
2) This cannot account for the discrepancies (Keller & Lamandé, 2010)
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21Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
Stress propagation in soil: Simulation vs. measurements (typical result)
Possible reasons (Keller & Lamandé, 2010):
(1) Upper model boundary condition is wrong
(2) Model for stress propagation is inappropriate
(3) Stress measurements are inaccurate
Keller T & Lamandé M (2010) Challenges in the development of analytical soil compaction models. Soil & Tillage Research 111, 54-64.
![Page 21: Eidgenössisches Volkswirtschaftsdepartement EVD Forschungsanstalt Agroscope Reckenholz-Tänikon ART 4a. Mechanical stresses during wheel traffic Thomas.](https://reader036.fdocuments.us/reader036/viewer/2022062511/551a83d85503466b3a8b4905/html5/thumbnails/21.jpg)
22Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
Stress propagation in soil: towards a 2-layer approach
A pragmatic model would be:
1) Tilled layer (e.g. 0-0.25 m depth): no stress attenuation
2) Subsoil: according to Söhne (1953)
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23
Simulations of σz
with different values for concentration factor (ν).
Field measure-ments of σz
Comparison:When (at which ν)
does the simulated σz
fit best the measured σz
(lowest RMSE)?
n
izzn
RMSE1
2ˆ1
Estimation of the concentration factor: Approach (i)
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
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24
ν = f (soil properties, loading)
Linear regression model(which soil properties and loading characteristics describe
best the optimized ν?)
Estimation of the concentration factor: Approach (ii)
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
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25
Regression for data from wheeling experiments on seven soils (12 -61% clay) yields:
σpc ↑ ν ↓
Sand ↑ ν ↑
σpc [kPa]
Sand [%]
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
Keller T, Stettler M, Arvidsson J, Lamandé M, Schjønning P, Berli M & Rydberg T (2009) Stress propagation in arable soil: determination and estimation of the concentration factor. Proc. 18th Conf. ISTRO, Izmir, Turkey, 15-19 June 2009.
Estimation of the concentration factor: Results from a preliminary study
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Federal Department of Economic Affairs FDEA
Agroscope Reckenholz-Tänikon Research Station ART
6c. WP1: Soil mechanical models and pedotransfer functions
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27
1. Model approach
2. Estimation of model parameters
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
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28
1. Modelling approach: a) upper model boundary condition (i)
?
Model ‘FRIDA’:(Keller, 2005; Schjønning et al. 2008)
Contact area
Stress distribution
1//|, nnbyaxyx
),(),(),,,,(),( yxgyxfnbaCFyx wheel
)(1),(
yl
xyxf
x
gm
xw
y
xw
yyxg
yy
/)(
1exp)(
1),(
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
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29Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
1. Modelling approach: a) upper model boundary condition (ii)
Empirical modelsfor each of the FRIDA modelparemeters
Upper model boundary condition
Easily-available tyre/loading properties (e.g., tyre dimensions, tyre inflation
pressure, wheel load) and information on soil condition/consistency
Model ‘FRIDA’:(Keller, 2005; Schjønning et al. 2008)
Parameters:
1. Contact area: l and w, n,
2. Stress distribution: α and
e.g.: = a Ptyre + b PWheelLoad
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30Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
1. Modelling approach: b) stress propagation
A new semi-empirical model:
1) Tilled layer (e.g. 0-0.25 m depth): no stress attenuation
2) Subsoil: according to Söhne (1953)
„Classical“ one-layer model (Söhne, 1953)
Compare, and select the best performing model…
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31
1. Modelling approach: c) compressive soil strength
Pragmatic model: CS = k x PCS
where:CS = compressive strength (kPa)PCS = precompression stress (kPa)k = empirical factor (-), k = 0..1
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
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32
1. Model approach
2. Estimation of model parameters
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
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33Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
2. Estimation of model parameters: a) upper model boundary condition (ii)
Data available:
Measurements from Sweden (Keller, 2005)Measurements from Denmark (Schjønning et al., 2006, 2008; Lamandé & Schjønning, 2008; Lamandé & Schjønning, in press)Unpublished data from Denmark [designed to study impacts of soil consistency] (Schjønning et al., unpublished)
Work to be done:
Compile data (mostly done)Find appropriate parameter (property) to characterize soil consistencyDevelop „tyre-transfer functions“ for estimation of FRIDA model parameters
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34Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
2. Estimation of model parameters: b) stress propagation
Data available:
Measurements from Sweden, using load cells (Keller, 2004; Keller & Arvidsson 2004, 2006; Keller & Lamandé, 2010)Measurements from Denmark, using load cells (Lamandé & Schjønning, 2007; Lamandé & Schjønning 1-3, in press; Keller & Lamandé, 2010)Measurements from Switzerland, using Bolling probes (Anken et al., 1993; Zihlmann et al., 1995, Diserens & Anken, 1995; Anken et al., 2000; Gysi et al., 2001; van der Veer, 2004; Schäffer et al., 2007)
Work to be done:
Compile data (mostly done)Correct stress readings (Berli et al., 2006; Lamandé et al., unpublished)Simulate stress and compare with measurements (i) best model (“2-layer” vs. “classical”), and (ii) concentration factorDevelop „pedo-transfer functions“ for estimation of the concentration factor
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35Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
2. Estimation of model parameters: c) soil strength
Data available:
Uniaxial compression from Switzerland (Weisskopf et al., unpublished), Sweden (Keller & Arvidsson, 2007; Keller et al., in press; Keller, unpublished) and Denmark (Schjønning, 1996; Schjønning & Lamandé, unpublished)In situ stress-strain data from Sweden (Keller, 2004; Keller & Arvidsson 2004,
2006; Keller & Lamandé, 2010) and Denmark (Lamandé & Schjønning, 2007; Lamandé & Schjønning 1-3, in press; Keller & Lamandé, 2010)
Work to be done:
Merge and harmonize data (mostly done)Agree on a proper method to obtain precompression stressDevelop „pedo-transfer functions“ for estimation of precompression stressFind the empirical factor “k” that relates soil strength to precompression stress
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Federal Department of Economic Affairs FDEA
Agroscope Reckenholz-Tänikon Research Station ART
7c. Structure of soil and weather data bases, Switzerland
Thomas Keller1,2 and Matthias Stettler3
1Agroscope Reckenholz-Tänikon Research Station ART, Reckenholzstrasse 191, CH-8046 Zürich, Switzerland; E-mail: [email protected]
2Swedish University of Agricultural Sciences, Department of Soil and Environment, Box 7014, SE-75007 Uppsala, Sweden
3Swiss College of Agriculture, Länggasse 85, CH-3052 Zollikofen, Switzerland
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A. Soil data
A national soil database does not exist…, but is in progress (however, to be expected after the end of PredICTor)…
Some counties („Kantons“) do have GIS-based soil maps ( perhaps this could be used as a pilot study area)
Best soil map of Switzerland: „Soil suitability map“ (suitability with regard to agricultural production; „Bodeneignungskarte“) 1:200‘000 Some counties do have soil maps 1:5‘000 to 1:25‘000
Problem: existing soil data and maps are rather descriptive (e.g. no exact values of clay content but only classes)
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
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B. Meteorological data
Agroscope ART has direct access to about 60 official (Meteo Switzerland) weather stations of Switzerland (hereby, data from these weather stations are mirrored to a database on an institute server every night)
The data includes prognosis of the coming two days
Data from the database could be accessed from Terranimo® (discussed and confirmed at a meeting in Zürich last October)
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART