eidgenössisches volkswirtschaftsdepartement evd forschungsanstalt agroscope reckenholz-tänikon art...

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

mailto:[email protected]



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...

3Kolloquium FB31 | BodenverdichtungThomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART

Stress propagation in soil

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

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®

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

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.


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.



(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

.

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


Simulated, using uniform stress distribution

Measured stress

Simulated, using measured stress distribution

12

0.0

0.2

0.4

0.6

0.8

1.0

0 50 100 150 200 250

De

pth

(m)


Stress distribution at the tyre-soil contact affects stress propagation


?

But…


Idea…

?

Model

Stress distribution

Easily-available tyre/loading properties (e.g., tyre dimensions, tyre inflation

pressure, wheel load) and information on soil condition/consistency


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


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),(

16

0.0

0.2

0.4

0.6

0.8

1.0

0 50 100 150 200 250


De

pth

(m

)Predicting stress in soil


Simulated, using uniform stress distribution

Measured stress

Simulated, using FRDIA generated stress distribution

Simulated, using measured stress distribution


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...

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



3Department of Agroecology, Aarhus University, Research Centre Foulum, P.O. Box 50, DK-8830 Tjele, Denmark






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)


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)

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)


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)


25

Regression for data from wheeling experiments on seven soils (12 -61% clay) yields:

σpc ↑ ν ↓

Sand ↑ ν ↑

σpc [kPa]

Sand [%]


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



6c. WP1: Soil mechanical models and pedotransfer functions

27

1. Model approach

2. Estimation of model parameters


28

1. Modelling approach: a) upper model boundary condition (i)

?


Contact area

Stress distribution

1//|, nnbyaxyx

),(),(),,,,(),( yxgyxfnbaCFyx wheel

)(1),(

yl

xyxf

x

gm

xw

y

xw

yyxg

yy

/)(

1exp)(

1),(



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


Parameters:

1. Contact area: l and w, n,

2. Stress distribution: α and

e.g.: = a Ptyre + b PWheelLoad


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…

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


32

1. Model approach

2. Estimation of model parameters



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


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


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



7c. Structure of soil and weather data bases, Switzerland

Thomas Keller1,2 and Matthias Stettler3







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)


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)


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