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: thomas.keller@art.admin.ch 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

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

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

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)

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)

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

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

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

Stress propagation: Söhne‘s summation procedure Pi zi σz Söhne W (1953) Druckverteilung im Boden und Bodenverformung unter Schlepperreifen. Grundlagen der Landtechnik 5, 49-63. Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

Stress propagation in soil ν = Concentration factor (Boussinesq, 1884; Fröhlich, 1934; Söhne, 1953) Söhne W (1953) Grundlagen der Landtechnik 5, 49-63. 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. Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART 10

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

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

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

Measuring stress distribution at the tyre-soil interface 1 2 3 4 Photos: Per Schjønning Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

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, 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. Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

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

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

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: thomas.keller@art.admin.ch 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

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, 54-64. Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

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, 54-64. 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

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, 54-64. Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

Stress propagation in soil: towards a 2-layer approach A pragmatic model would be: Tilled layer (e.g. 0-0.25 m depth): no stress attenuation Subsoil: according to Söhne (1953) Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

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

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

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, 15-19 June 2009. Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

6c. WP1: Soil mechanical models and pedotransfer functions

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

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

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

1. Modelling approach: b) stress propagation A new semi-empirical model: Tilled layer (e.g. 0-0.25 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

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

Estimation of model parameters Model approach Estimation of model parameters Thomas 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 consistency Develop „tyre-transfer functions“ for estimation of FRIDA model parameters Thomas 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 factor Develop „pedo-transfer functions“ for estimation of the concentration factor Thomas 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 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

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: thomas.keller@art.admin.ch 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

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

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