1. 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 Zürich, Switzerland; Swedish University of Agricultural Sciences, Department of Soil and Environment, Box 7014, SE Uppsala, Sweden 3Department of Agroecology, Aarhus University, Research Centre Foulum, P.O. Box 50, DK Tjele, Denmark 4Swiss College of Agriculture, Länggasse 85, CH-3052 Zollikofen, Switzerland

2. Soil compaction in three steps...
Contact tyre/track-soil = Upper model boundary condition:
Contact area
Stress distribution
Stress propagation
Stress-strain (void ratio) relationship & Mechanical soil strength
Stress > Strength  Compaction
Stress < Strength  Elastic deformation
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

3. Stress propagation in soil
Kolloquium FB31 | Bodenverdichtung
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

4. Modelling stress propagation
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)
Analytical solutions
Simple and robust
3-Dimensional
Limitations:
Elastic theory
(e.g. Keller & Lamandé 2010, Soil & Tillage Research 111)

5. Modelling stress propagation
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)
Suitable for easily-applicable decision support tools
 Approach in Terranimo®
Analytical solutions
Simple and robust
3-Dimensional
Limitations:
Elastic theory
(e.g. Keller & Lamandé 2010, Soil & Tillage Research 111)

6. Numerical methods…
Finite elemente method (FEM) Discrete element method (DEM)
From Jean-Yves Delenne (University of Montpellier, Frankreich)
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

7. Stress propagation: point load
For elastic material (Boussinesq, 1885): y x r Ѳ σr z
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

8. Stress propagation: point load
Soil is not fully elastic… Therefore (Fröhlich, 1934): x y z r Ѳ P σr
ν = „concentration factor“
(empirical factor)
Fröhlich OK (1934) Druckverteilung im Baugrunde. Springer Verlag, Wien, 178 pp.
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

9. Stress propagation: Söhne‘s summation procedurePi zi σz
Söhne W (1953) Druckverteilung im Boden und Bodenverformung unter Schlepperreifen. Grundlagen der Landtechnik 5,
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

10. Stress propagation in soil
ν = Concentration factor
(Boussinesq, 1884; Fröhlich, 1934; Söhne, 1953)
Söhne W (1953) Grundlagen der Landtechnik 5,
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,
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART 10

11. Stress distribution at the tyre-soil contact affects stress propagation
Simulated, using
measured stress distribution
Simulated, using
uniform stress distribution
Measured stress
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

12. Stress distribution at the tyre-soil contact affects stress propagation?
But…
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

13. Idea…
Easily-available tyre/loading properties (e.g., tyre dimensions, tyre inflation pressure, wheel load) and information on soil condition/consistency ?
Model
Stress distribution
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

14. Measuring stress distribution at the tyre-soil interface1 2 3 4
Photos: Per Schjønning
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

15. Tyre: 800/50 R34; Wheel load: 6000 kg
Upper model boundary condition: Model „FRIDA“
Model ‘FRIDA’:
(Keller, 2005; Schjønning et al. 2008)
Contact area
Stress distribution
Tyre: 800/50 R34; Wheel load: 6000 kg
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,
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,
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

16. Predicting stress in soil
Simulated, using
measured stress distribution
Simulated, using FRDIA
generated stress distribution
Simulated, using
uniform stress distribution
Measured stress
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

17. Soil compaction in three steps...
Contact tyre/track-soil = Upper model boundary condition:
Contact area
Stress distribution
Stress propagation
Stress-strain (void ratio) relationship & Mechanical soil strength
Stress > Strength  Compaction
Stress < Strength  Elastic deformation
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

18. 6a. Stress transmission Thomas Keller1,2, Mathieu Lamandé3, Matthias Stettler4 and Per Schjønning3   1Agroscope Reckenholz-Tänikon Research Station ART, Reckenholzstrasse 191, CH Zürich, Switzerland; Swedish University of Agricultural Sciences, Department of Soil and Environment, Box 7014, SE Uppsala, Sweden 3Department of Agroecology, Aarhus University, Research Centre Foulum, P.O. Box 50, DK Tjele, Denmark 4Swiss College of Agriculture, Länggasse 85, CH-3052 Zollikofen, Switzerland

19. Stress propagation in soil: Simulation vs
Stress propagation in soil: Simulation vs. measurements (typical result)
Possible reasons (Keller & Lamandé, 2010):
Upper model boundary condition is wrong
Model for stress propagation is inappropriate
Stress measurements are inaccurate
Keller T & Lamandé M (2010) Challenges in the development of analytical soil compaction models. Soil & Tillage Research 111,
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

20. Stress propagation in soil: Simulation vs
Stress propagation in soil: Simulation vs. measurements (typical result)
FRIDA
Possible reasons (Keller & Lamandé, 2010):
Upper model boundary condition is wrong
Model for stress propagation is inappropriate
Stress measurements are inaccurate
Keller T & Lamandé M (2010) Challenges in the development of analytical soil compaction models. Soil & Tillage Research 111,
We know that we are within  10% (Lamandé et al., unpublished)
This cannot account for the discrepancies (Keller & Lamandé, 2010)
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

21. Stress propagation in soil: Simulation vs
Stress propagation in soil: Simulation vs. measurements (typical result)
Possible reasons (Keller & Lamandé, 2010):
Upper model boundary condition is wrong
Model for stress propagation is inappropriate
Stress measurements are inaccurate
Keller T & Lamandé M (2010) Challenges in the development of analytical soil compaction models. Soil & Tillage Research 111,
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

22. Stress propagation in soil: towards a 2-layer approach
A pragmatic model would be:
Tilled layer (e.g m depth): no stress attenuation
Subsoil: according to Söhne (1953)
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

23. Estimation of the concentration factor: Approach (i)
Field measure-ments of σz
Simulations of σz with different values for concentration factor (ν).
Comparison:
When (at which ν) does the simulated σz
fit best the measured σz
(lowest RMSE)?
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

24. Estimation of the concentration factor: Approach (ii)
ν = f (soil properties, loading)
Linear regression model
(which soil properties and loading characteristics describe best the optimized ν?)
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

25. Estimation of the concentration factor: Results from a preliminary study
Regression for data from wheeling experiments on seven soils (12 -61% clay) yields:
σpc [kPa]
Sand [%]
σpc ↑  ν ↓
Sand ↑  ν ↑
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, June 2009.
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

26. 6c. WP1: Soil mechanical models and pedotransfer functions

27. Estimation of model parameters
Model approach
Estimation of model parameters
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

28. 1. Modelling approach: a) upper model boundary condition (i)
Model ‘FRIDA’:
(Keller, 2005; Schjønning et al. 2008)
Contact area
Stress distribution ?
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

29. 1. Modelling approach: a) upper model boundary condition (ii)
Easily-available tyre/loading properties (e.g., tyre dimensions, tyre inflation pressure, wheel load) and information on soil condition/consistency
Empirical models
for each of the
FRIDA model
paremeters
Upper model boundary condition
e.g.:  = a Ptyre + b PWheelLoad
Model ‘FRIDA’:
(Keller, 2005; Schjønning et al. 2008)
Parameters:
Contact area: l and w, n,
Stress distribution: α and 
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

30. 1. Modelling approach: b) stress propagation
A new semi-empirical model:
Tilled layer (e.g m depth): no stress attenuation
Subsoil: according to Söhne (1953)
Compare, and select the best performing model…
„Classical“ one-layer model (Söhne, 1953)
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

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

32. Estimation of model parameters
Model approach
Estimation of model parameters
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

33. 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 consistency
Develop „tyre-transfer functions“ for estimation of FRIDA model parameters
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

34. 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 factor
Develop „pedo-transfer functions“ for estimation of the concentration factor
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

35. 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 stress
Develop „pedo-transfer functions“ for estimation of precompression stress
Find the empirical factor “k” that relates soil strength to precompression stress
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

36. 7c. Structure of soil and weather data bases, Switzerland Thomas Keller1,2 and Matthias Stettler3   1Agroscope Reckenholz-Tänikon Research Station ART, Reckenholzstrasse 191, CH Zürich, Switzerland; Swedish University of Agricultural Sciences, Department of Soil and Environment, Box 7014, SE Uppsala, Sweden 3Swiss College of Agriculture, Länggasse 85, CH-3052 Zollikofen, Switzerland

37. 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

38. 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