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: 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, DK8830 Tjele, Denmark
4Swiss
College of Agriculture, Länggasse 85, CH-3052 Zollikofen, Switzerland
Soil compaction in three steps...
1.
Contact tyre/track-soil = Upper
model boundary condition:


Contact area
Stress distribution
0
0.5
1
Log stress (kPa)
1.5
2
2.5
3
3.5
0.7
Stress propagation
Void ratio
2.
0.6
0.5
0.4
3.
Stress-strain (void ratio) relationship &
Mechanical soil strength


Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
Stress > Strength  Compaction
Stress < Strength  Elastic deformation
2
Stress propagation in soil
Kolloquium FB31 | Bodenverdichtung
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
3
Modelling stress propagation
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
4
102)
Modelling stress propagation
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
Suitable
Elasto-plastic
stress-strain relationships
for easily(e.g.
Modified
Cam Clay)
applicable
decision
support
tools
Can account for stress-dependent
material
properties
 Approach
in Terranimo®
 Limitations:
• Description of tyre-soil contact
• Parameterization
(e.g. Richards & Peth 2009, Soil & Tillage Research
5
102)
Stress propagation: point load
P
For elastic material (Boussinesq, 1885):
y
3P
r 
cos 
2
2r
x
Ѳ
r
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
7
Stress propagation: point load
Soil is not fully elastic… Therefore
(Fröhlich, 1934):
P
 2
r 
cos

2
2r
P
y
ν = „concentration factor“
(empirical factor)
x
Ѳ
r
σr
z
Fröhlich OK (1934) Druckverteilung im Baugrunde. Springer Verlag, Wien, 178 pp.
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
8
Stress propagation: Söhne‘s
summation procedure
Pi
zi
Pi
 2
z  
cos
i
2
i  0 2zi
i n
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
9
Stress propagation in soil
Pi
 2
r  
cos
i
2
i 0 2ri
Söhne W (1953) Grundlagen der Landtechnik 5, 49-63.
i n
(Boussinesq, 1884; Fröhlich, 1934; Söhne,
1953)
ν = Concentration factor
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
Vertical stress (kPa)
measured stress distribution
0
50
Simulated, using
0.0
uniform stress distribution
100
150
200
250
Depth (m)
0.2
0.4
0.6
Measured stress
0.8
1.0
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
11
Stress distribution at the tyre-soil
contact affects stress propagation
Vertical stress (kPa)
0
50
100
150
200
250
0.0
Depth (m)
0.2
0.4
0.6
But…
0.8
1.0
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
?
12
Idea…
Easily-available tyre/loading properties
(e.g., tyre dimensions, tyre inflation
pressure, wheel load) and information on
soil condition/consistency
?
Stress distribution
Model
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
13
Measuring stress distribution at the tyresoil interface
1
4 250
Gemessener Druck (kPa)
3
2
Fahrtrichtung
200
150
100
50
59
29
0
Photos: Per Schjønning
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
0
34
-59
68
...
-29
te
34
0
Länge
(cm)
B
re
i
68
14
Upper model boundary condition: Model
„FRIDA“
Tyre: 800/50 R34; Wheel
load: 6000
kg
Model
‘FRIDA’:
(Keller, 2005; Schjønning et al. 2008)
Contact area
Measured


   x, y  | x / a  y / b  1
n
n
Stress distribution
 ( x, y) Fwheel C ( ,  , a, b, n) f ( x, y) g ( x, y)



x
f ( x, y)  1 

 l x ( y) 
Modelled

y
g ( x, y )  1 

wy ( x)




 exp    1  y



wy ( x)





  / gm



Keller T (2005) A model for prediction of the contact area and the distribution of vertical stress below agricultural tyres from readilyavailable 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
15
Predicting stress in soil
Simulated, using
measured stress distribution
Simulated, using FRDIA
generated stress distribution
Vertical stress (kPa)
0
50
Simulated, using
0.0
uniform stress distribution
100
150
200
250
Depth (m)
0.2
0.4
0.6
Measured stress
0.8
1.0
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
16
Soil compaction in three steps...
1.
Contact tyre/track-soil = Upper
model boundary condition:


Contact area
Stress distribution
0
0.5
1
Log stress (kPa)
1.5
2
2.5
3
3.5
0.7
Stress propagation
Void ratio
2.
0.6
0.5
0.4
3.
Stress-strain (void ratio) relationship &
Mechanical soil strength


Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
Stress > Strength  Compaction
Stress < Strength  Elastic deformation
17
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: 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, DK8830 Tjele, Denmark
4Swiss
College of Agriculture, Länggasse 85, CH-3052 Zollikofen, Switzerland
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.
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
19
Stress propagation in soil: Simulation
vs. measurements (typical result)
FRIDA
1) We know that we are
within  10% (Lamandé et
al., unpublished)
2) This cannot account for
the discrepancies (Keller
& Lamandé, 2010)
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.
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
20
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.
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
21
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)
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
22
Estimation of the concentration factor:
Approach (i)
Field measurements 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)?
1 n
2
ˆ


RMSE 



 z z
n i 1
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
23
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
24
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 ↑
Sand ↑


ν↓
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
25
Federal Department of Economic Affairs FDEA
Agroscope Reckenholz-Tänikon Research Station ART
6c.
WP1: Soil mechanical models and
pedotransfer functions
1. Model approach
2. Estimation of model
parameters
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
27
1. Modelling approach: a) upper model
boundary condition (i)
Model ‘FRIDA’:
(Keller, 2005; Schjønning et al. 2008)
Contact area


   x, y  | x / a  y / b  1
n
n
Stress distribution
 ( x, y) Fwheel C ( ,  , a, b, n) f ( x, y) g ( x, y)
?



x


f ( x, y)  1 

l x ( y) 




y
g ( x, y )  1 

wy ( x)

Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART



 exp    1  y



wy ( x)





  / gm



28
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 e.g.:  = a Ptyre + b PWheelLoad
for each of the
FRIDA model
paremeters
Model ‘FRIDA’:
Upper model
boundary condition
(Keller, 2005; Schjønning et al. 2008)
Parameters:
1. Contact area: l and w, n,
2. Stress distribution: α and 
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
29
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)
Compare, and select the
best performing model…
„Classical“ one-layer
model (Söhne, 1953)
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
30
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
31
1. Model approach
2. Estimation of model
parameters
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
32
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
33
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 (“2layer” vs. “classical”), and (ii) concentration factor
Develop „pedo-transfer functions“ for estimation of the concentration
factor
Thomas Keller | © Agroscope Reckenholz-Tänikon Research Station ART
34
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
35
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: 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
37
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
38